1
What is the sum of the first 7 terms of a geometric sequence with first term -2 and common ratio 4?
Medium
ExplanationSum = a₁(rⁿ − 1)/(r − 1) = -2((4)^7 − 1)/(4 − 1) = -10922.
2
f(x) = -8x + 9 if x < -8, and f(x) = -6x + 14 if x ≥ -8. What is f(-8)?
Medium
ExplanationSince -8 ≥ -8, use f(x) = -6x + 14: f(-8) = 62.
3
A sequence is defined by a₁ = -1 and aₙ = aₙ₋₁ + 10 for n > 1. What is a11?
Medium
ExplanationEach term adds 10 to the previous one, so a11 = a₁ + (11−1)(10) = 99.
4
An employee's salary starts at Rs. 36698 and increases by Rs. 3793 each year. What will the salary be after 15 years?
Medium
ExplanationSalary after 15 years = 36698 + 15 × 3793 = Rs. 93593.
5
If f(x) = -6x + 7, for what value of x does f(x) = -5?
Medium
Explanation-6x + 7 = -5, so x = 2.
6
If f(x) = -x^2 − 2x − 10, what is f(8)?
Medium
Explanationf(8) = -1(8)^2 + (-2)(8) + (-10) = -90.
7
An arithmetic sequence has first term 43 and common difference -11. What is the 25th term?
Medium
Explanationaₙ = a₁ + (n−1)d = 43 + (25−1)(-11) = -221.
8
Is the sequence 10, 0, -1, -9, ... arithmetic, geometric, or neither?
Medium
ExplanationThere is no constant common difference or common ratio between terms, so this sequence is neither arithmetic nor geometric.
9
In an arithmetic sequence, the 15th term is -78 and the 32nd term is -231. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-231 − (-78))/(32−15) = -9.
10
A geometric sequence has first term -5 and common ratio -2. What is the 6th term?
Medium
Explanationaₙ = a₁ × r^(n−1) = -5 × (-2)^5 = 160.
— Sponsored —
11
If f(x) = 3x^2 + 2x − 12, what is f(-4)?
Medium
Explanationf(-4) = 3(-4)^2 + (2)(-4) + (-12) = 28.
12
An employee's salary starts at Rs. 24527 and increases by Rs. 2187 each year. What will the salary be after 15 years?
Medium
ExplanationSalary after 15 years = 24527 + 15 × 2187 = Rs. 57332.
13
What is the sum to infinity of a geometric sequence with first term -5 and common ratio 2/5?
Medium
ExplanationSum to infinity = a₁/(1 − r) = -5/(1 − 2/5) = -25/3.
14
If f(x) = -3x − 14 and g(x) = f(x + 5) − 6, what is g(-15)?
Medium
Explanationg(-15) = f(-10) − 6 = 16 − 6 = 10.
15
An employee's salary starts at Rs. 45810 and increases by Rs. 2855 each year. What will the salary be after 4 years?
Medium
ExplanationSalary after 4 years = 45810 + 4 × 2855 = Rs. 57230.
16
If f(x) = 6x − 8, for what value of x does f(x) = -92?
Medium
Explanation6x − 8 = -92, so x = -14.
17
Is the sequence 13, 26, 52, 104, ... arithmetic, geometric, or neither?
Medium
ExplanationEach term is a constant multiple of the previous one, so this sequence is geometric.
18
For the function f(x) = √(x − 73), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − 73 ≥ 0, so x ≥ 73. The smallest such value is 73.
19
If f(x) = 2x − 5 and g(x) = f(x + 8) − 5, what is g(5)?
Medium
Explanationg(5) = f(13) − 5 = 21 − 5 = 16.
20
f(x) = 4x + 6 if x < -2, and f(x) = -5x + 9 if x ≥ -2. What is f(2)?
Medium
ExplanationSince 2 ≥ -2, use f(x) = -5x + 9: f(2) = -1.
— Sponsored —
21
f(x) = 2x + 4 if x < 4, and f(x) = -2x − 2 if x ≥ 4. What is f(-7)?
Medium
ExplanationSince -7 < 4, use f(x) = 2x + 4: f(-7) = -10.
22
In an arithmetic sequence, the 10th term is -44 and the 23rd term is -135. What is the 13th term?
Medium
Explanationd = (-135 − (-44))/(23−10) = -7. Then the 13th term = -44 + (13−10)(-7) = -65.
23
For the function f(x) = 1/(x − (-27)), which value of x must be excluded from the domain?
Medium
ExplanationThe denominator x − (-27) cannot equal 0, so x = -27 must be excluded from the domain.
24
In an arithmetic sequence, the 6th term is -28 and the 19th term is -132. What is the 29th term?
Medium
Explanationd = (-132 − (-28))/(19−6) = -8. Then the 29th term = -28 + (29−6)(-8) = -212.
25
In an arithmetic sequence, the 4th term is 38 and the 18th term is 122. What is the 29th term?
Medium
Explanationd = (122 − 38)/(18−4) = 6. Then the 29th term = 38 + (29−4)(6) = 188.
26
If f(x) = -7x − 11, what is f(5) − f(-2)?
Medium
Explanationf(5) = -46 and f(-2) = 3, so f(5) − f(-2) = -49.
27
If f(x) = 6x − 20, what is f⁻¹(40)?
Medium
Explanationf⁻¹(40) is the x-value such that f(x) = 40: 6x − 20 = 40, so x = 10.
28
If f(x) = 6x^2 − 8x + 3, what is f(6)?
Medium
Explanationf(6) = 6(6)^2 + (-8)(6) + (3) = 171.
29
If f(x) = -6x + 17, what is f(9) + f(5)?
Medium
Explanationf(9) = -37 and f(5) = -13, so f(9) + f(5) = -50.
30
If f(x) = -4x + 7 and g(x) = f(x + 1) − 7, what is g(5)?
Medium
Explanationg(5) = f(6) − 7 = -17 − 7 = -24.
— Sponsored —
31
In an arithmetic sequence, the 7th term is -22 and the 15th term is -62. What is the 17th term?
Medium
Explanationd = (-62 − (-22))/(15−7) = -5. Then the 17th term = -22 + (17−7)(-5) = -72.
32
In an arithmetic sequence, the 7th term is -29 and the 15th term is -77. What is the 30th term?
Medium
Explanationd = (-77 − (-29))/(15−7) = -6. Then the 30th term = -29 + (30−7)(-6) = -167.
33
f(x) = -5x + 10 if x < -2, and f(x) = -2x + 11 if x ≥ -2. What is f(-8)?
Medium
ExplanationSince -8 < -2, use f(x) = -5x + 10: f(-8) = 50.
34
If f(x) = 6x − 2, what is f⁻¹(-32)?
Medium
Explanationf⁻¹(-32) is the x-value such that f(x) = -32: 6x − 2 = -32, so x = -5.
35
In an arithmetic sequence, the 8th term is 3 and the 11th term is -12. What is the 9th term?
Medium
Explanationd = (-12 − 3)/(11−8) = -5. Then the 9th term = 3 + (9−8)(-5) = -2.
36
An employee's salary starts at Rs. 21602 and increases by Rs. 1469 each year. What will the salary be after 10 years?
Medium
ExplanationSalary after 10 years = 21602 + 10 × 1469 = Rs. 36292.
37
An employee's salary starts at Rs. 49554 and increases by Rs. 518 each year. What will the salary be after 14 years?
Medium
ExplanationSalary after 14 years = 49554 + 14 × 518 = Rs. 56806.
38
In an arithmetic sequence, the 6th term is -57 and the 8th term is -73. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-73 − (-57))/(8−6) = -8.
39
A sequence is defined by a₁ = -10 and aₙ = aₙ₋₁ + 7 for n > 1. What is a14?
Medium
ExplanationEach term adds 7 to the previous one, so a14 = a₁ + (14−1)(7) = 81.
40
If f(x) = 6x + 7 and g(x) = -4x − 11, what is f(g(3))?
Medium
Explanationg(3) = -23, so f(g(3)) = f(-23) = 6(-23) + 7 = -131.
— Sponsored —
41
If f(x) = -12x + 3, for what value of x does f(x) = -237?
Medium
Explanation-12x + 3 = -237, so x = 20.
42
If f(x) = 3x + 1, what is f⁻¹(10)?
Medium
Explanationf⁻¹(10) is the x-value such that f(x) = 10: 3x + 1 = 10, so x = 3.
43
If f(x) = 2x + 7, for what value of x does f(x) = -5?
Medium
Explanation2x + 7 = -5, so x = -6.
44
f(x) = 7x + 2 if x < 4, and f(x) = -2x + 1 if x ≥ 4. What is f(0)?
Medium
ExplanationSince 0 < 4, use f(x) = 7x + 2: f(0) = 2.
45
In an arithmetic sequence, the 11th term is 60 and the 18th term is 95. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (95 − 60)/(18−11) = 5.
46
If f(x) = 11x − 21, for what value of x does f(x) = 12?
Medium
Explanation11x − 21 = 12, so x = 3.
47
If f(x) = -5x + 12 and g(x) = f(x + 12) + 14, what is g(10)?
Medium
Explanationg(10) = f(22) + 14 = -98 + 14 = -84.
48
If f(x) = 6x + 22, what is f(-15)?
Medium
Explanationf(-15) = (6)(-15) + 22 = -68.
49
In an arithmetic sequence, the 5th term is -30 and the 14th term is -120. What is the 18th term?
Medium
Explanationd = (-120 − (-30))/(14−5) = -10. Then the 18th term = -30 + (18−5)(-10) = -160.
50
What is the sum to infinity of a geometric sequence with first term -14 and common ratio 2/5?
Medium
ExplanationSum to infinity = a₁/(1 − r) = -14/(1 − 2/5) = -70/3.
— Sponsored —
51
For the function f(x) = √(x − 69), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − 69 ≥ 0, so x ≥ 69. The smallest such value is 69.
52
In an arithmetic sequence, the 10th term is -50 and the 24th term is -92. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-92 − (-50))/(24−10) = -3.
53
For the function f(x) = √(x − 36), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − 36 ≥ 0, so x ≥ 36. The smallest such value is 36.
54
If f(x) = 8x − 22, what is f(-9)?
Medium
Explanationf(-9) = (8)(-9) − 22 = -94.
55
In an arithmetic sequence, the 5th term is 14 and the 16th term is 47. What is the 26th term?
Medium
Explanationd = (47 − 14)/(16−5) = 3. Then the 26th term = 14 + (26−5)(3) = 77.
56
In an arithmetic sequence, the 7th term is 4 and the 18th term is 15. What is the 10th term?
Medium
Explanationd = (15 − 4)/(18−7) = 1. Then the 10th term = 4 + (10−7)(1) = 7.
57
If f(x) = -11x + 8, for what value of x does f(x) = 74?
Medium
Explanation-11x + 8 = 74, so x = -6.
58
A population of 512 grows by 50% each year. What will the population be after 4 years?
Medium
ExplanationPopulation after 4 years = 512 × (1 + 50/100)^4 = 2592.
59
If f(x) = -6x + 8 and g(x) = f(x + 5) + 1, what is g(-5)?
Medium
Explanationg(-5) = f(0) + 1 = 8 + 1 = 9.
60
An employee's salary starts at Rs. 60981 and increases by Rs. 3975 each year. What will the salary be after 8 years?
Medium
ExplanationSalary after 8 years = 60981 + 8 × 3975 = Rs. 92781.
— Sponsored —
61
In an arithmetic sequence, the 7th term is -39 and the 16th term is -138. What is the 21st term?
Medium
Explanationd = (-138 − (-39))/(16−7) = -11. Then the 21st term = -39 + (21−7)(-11) = -193.
62
In an arithmetic sequence, the 12th term is -40 and the 22nd term is -110. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-110 − (-40))/(22−12) = -7.
63
A geometric sequence has first term 1 and common ratio 3. What is the 6th term?
Medium
Explanationaₙ = a₁ × r^(n−1) = 1 × (3)^5 = 243.
64
An employee's salary starts at Rs. 40345 and increases by Rs. 3722 each year. What will the salary be after 15 years?
Medium
ExplanationSalary after 15 years = 40345 + 15 × 3722 = Rs. 96175.
65
For the function f(x) = √(x − (-58)), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − (-58) ≥ 0, so x ≥ -58. The smallest such value is -58.
66
What is the sum of the first 29 terms of an arithmetic sequence with first term -24 and common difference 5?
Medium
ExplanationThe 29th term is 116. Sum = n(a₁ + aₙ)/2 = 29(-24 + 116)/2 = 1334.
67
If f(x) = 7x − 13, for what value of x does f(x) = -146?
Medium
Explanation7x − 13 = -146, so x = -19.
68
If f(x) = 8x + 4 and g(x) = 2x + 2, what is g(f(3))?
Medium
Explanationf(3) = 28, so g(f(3)) = g(28) = 2(28) + 2 = 58.
69
If f(x) = -7x − 18, what is f(-8)?
Medium
Explanationf(-8) = (-7)(-8) − 18 = 38.
70
For the function f(x) = √(x − (-29)), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − (-29) ≥ 0, so x ≥ -29. The smallest such value is -29.
— Sponsored —
71
A geometric sequence has first term -7 and common ratio 2. What is the 7th term?
Medium
Explanationaₙ = a₁ × r^(n−1) = -7 × (2)^6 = -448.
72
If f(x) = -5x + 19, for what value of x does f(x) = 79?
Medium
Explanation-5x + 19 = 79, so x = -12.
73
In an arithmetic sequence, the 11th term is 92 and the 26th term is 257. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (257 − 92)/(26−11) = 11.
74
If f(x) = -x − 11, what is f(3) + f(1)?
Medium
Explanationf(3) = -14 and f(1) = -12, so f(3) + f(1) = -26.
75
f(x) = -2x − 12 if x < -6, and f(x) = -6x + 6 if x ≥ -6. What is f(-2)?
Medium
ExplanationSince -2 ≥ -6, use f(x) = -6x + 6: f(-2) = 18.
76
If f(x) = 4x + 3 and g(x) = f(x − 7) + 2, what is g(-11)?
Medium
Explanationg(-11) = f(-18) + 2 = -69 + 2 = -67.
77
For the function f(x) = √(x − (-28)), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − (-28) ≥ 0, so x ≥ -28. The smallest such value is -28.
78
What is the sum of the first 28 terms of an arithmetic sequence with first term 15 and common difference -8?
Medium
ExplanationThe 28th term is -201. Sum = n(a₁ + aₙ)/2 = 28(15 + (-201))/2 = -2604.
79
If f(x) = -7x − 15 and g(x) = f(x + 11) + 11, what is g(5)?
Medium
Explanationg(5) = f(16) + 11 = -127 + 11 = -116.
80
If f(x) = 2x − 13, what is f⁻¹(9)?
Medium
Explanationf⁻¹(9) is the x-value such that f(x) = 9: 2x − 13 = 9, so x = 11.
— Sponsored —
81
A population of 12000 grows by 10% each year. What will the population be after 3 years?
Medium
ExplanationPopulation after 3 years = 12000 × (1 + 10/100)^3 = 15972.
82
For the function f(x) = 1/(x − 14), which value of x must be excluded from the domain?
Medium
ExplanationThe denominator x − 14 cannot equal 0, so x = 14 must be excluded from the domain.
83
An employee's salary starts at Rs. 68071 and increases by Rs. 711 each year. What will the salary be after 11 years?
Medium
ExplanationSalary after 11 years = 68071 + 11 × 711 = Rs. 75892.
84
What is the sum of the first 5 terms of a geometric sequence with first term 1 and common ratio 4?
Medium
ExplanationSum = a₁(rⁿ − 1)/(r − 1) = 1((4)^5 − 1)/(4 − 1) = 341.
85
For the function f(x) = √(x − (-61)), what is the smallest value of x in the domain?
Medium
ExplanationThe expression under the square root must be ≥ 0: x − (-61) ≥ 0, so x ≥ -61. The smallest such value is -61.
86
f(x) = -5x + 7 if x < 5, and f(x) = 3x − 7 if x ≥ 5. What is f(2)?
Medium
ExplanationSince 2 < 5, use f(x) = -5x + 7: f(2) = -3.
87
If f(x) = 6x − 10, what is f(13) + f(-8)?
Medium
Explanationf(13) = 68 and f(-8) = -58, so f(13) + f(-8) = 10.
88
If f(x) = -x − 15 and g(x) = f(x − 3) + 13, what is g(-6)?
Medium
Explanationg(-6) = f(-9) + 13 = -6 + 13 = 7.
89
Is the sequence -8, -4, -6, -1, ... arithmetic, geometric, or neither?
Medium
ExplanationThere is no constant common difference or common ratio between terms, so this sequence is neither arithmetic nor geometric.
90
An arithmetic sequence has first term -1 and common difference 7. What is the 22nd term?
Medium
Explanationaₙ = a₁ + (n−1)d = -1 + (22−1)(7) = 146.
— Sponsored —
91
In an arithmetic sequence, the 6th term is 73 and the 21st term is 208. What is the 19th term?
Medium
Explanationd = (208 − 73)/(21−6) = 9. Then the 19th term = 73 + (19−6)(9) = 190.
92
An employee's salary starts at Rs. 48958 and increases by Rs. 4741 each year. What will the salary be after 5 years?
Medium
ExplanationSalary after 5 years = 48958 + 5 × 4741 = Rs. 72663.
93
If f(x) = 2x + 12 and g(x) = f(x + 5) − 8, what is g(-9)?
Medium
Explanationg(-9) = f(-4) − 8 = 4 − 8 = -4.
94
If f(x) = 6x − 14, for what value of x does f(x) = -8?
Medium
Explanation6x − 14 = -8, so x = 1.
95
If f(x) = -6x − 3 and g(x) = f(x + 3) + 10, what is g(1)?
Medium
Explanationg(1) = f(4) + 10 = -27 + 10 = -17.
96
Is the sequence 3, -6, 12, -24, ... arithmetic, geometric, or neither?
Medium
ExplanationEach term is a constant multiple of the previous one, so this sequence is geometric.
97
A geometric sequence has first term -8 and common ratio 2. What is the 7th term?
Medium
Explanationaₙ = a₁ × r^(n−1) = -8 × (2)^6 = -512.
98
What is the sum of the first 5 terms of a geometric sequence with first term 7 and common ratio -2?
Medium
ExplanationSum = a₁(rⁿ − 1)/(r − 1) = 7((-2)^5 − 1)/(-2 − 1) = 77.
99
If f(x) = -4x − 13 and g(x) = f(x − 2) + 4, what is g(13)?
Medium
Explanationg(13) = f(11) + 4 = -57 + 4 = -53.
100
In an arithmetic sequence, the 13th term is -210 and the 28th term is -420. What is the common difference?
Medium
Explanationd = (aⱼ − aᵢ)/(j−i) = (-420 − (-210))/(28−13) = -14.