CBSE Class 10 Mathematics Arithmetic Progressions MCQs Set 22

Practice MCQs for Class 10 Mathematics Chapter 05 Arithmetic Progressions

Review structured MCQ sets for Class 10 Mathematics Chapter 05 Arithmetic Progressions. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Access Chapter 05 Arithmetic Progressions Questions and Solutions

View or download the dedicated Chapter 05 Arithmetic Progressions MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: The first four terms of the sequence with a_n = 3n + 2 are
(a) 3, 6, 9, 12
(b) 5, 8, 11, 14
(c) 2, 5, 8, 11
(d) 5, 9, 13, 17
Show Answer & Explanation

Answer: (b) 5, 8, 11, 14

Explanation:
1. Put n = 1, 2, 3, 4: 5, 8, 11, 14.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 2: The first four terms of the sequence with a_n = 3ⁿ are
(a) 1, 3, 9, 27
(b) 3, 9, 27, 81
(c) 3, 6, 9, 12
(d) 3, 9, 81, 243
Show Answer & Explanation

Answer: (b) 3, 9, 27, 81

Explanation:
1. Put n = 1, 2, 3, 4: 3, 9, 27, 81.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 3: The first four terms of the sequence with a_n = (−1)ⁿ · 2ⁿ are
(a) 2, 4, 8, 16
(b) −2, −4, −8, −16
(c) −2, 4, −8, 16
(d) 2, −4, 8, −16
Show Answer & Explanation

Answer: (c) −2, 4, −8, 16

Explanation:
1. n = 1: −2; n = 2: 4; n = 3: −8; n = 4: 16.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 4: The first four terms of the sequence with a_n = n² − n + 1 are
(a) 1, 4, 9, 16
(b) 0, 2, 6, 12
(c) 1, 3, 5, 7
(d) 1, 3, 7, 13
Show Answer & Explanation

Answer: (d) 1, 3, 7, 13

Explanation:
1. n = 1: 1; n = 2: 3; n = 3: 7; n = 4: 13.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 5: The general term of a sequence is a_n = −4n + 15. The sequence is an A.P. with common difference and 15th term equal to
(a) d = 4 and a₁₅ = 45
(b) d = −4 and a₁₅ = −60
(c) d = −4 and a₁₅ = −45
(d) d = 15 and a₁₅ = −45
Show Answer & Explanation

Answer: (c) d = −4 and a₁₅ = −45

Explanation:
1. a_{n+1} − a_n = −4(n + 1) + 15 − (−4n + 15) = −4, a constant, so it is an A.P. The 15th term is −4(15) + 15 = −45.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 6: The first term of an A.P. is 5, the common difference is 3 and the last term is 80. The number of terms is
(a) 25
(b) 27
(c) 24
(d) 26
Show Answer & Explanation

Answer: (d) 26

Explanation:
1. 80 = 5 + (n − 1)3 gives (n − 1) = 25, so n = 26.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 7: The 10th term of the A.P. 1, 4, 7, 10, ... is
(a) 31
(b) 30
(c) 25
(d) 28
Show Answer & Explanation

Answer: (d) 28

Explanation:
1. a = 1, d = 3. a₁₀ = 1 + 9(3) = 28.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 8: The nth term of the A.P. 13, 8, 3, −2, ... is
(a) 13 − 5n
(b) 5n − 18
(c) 18 − 5n
(d) 18 + 5n
Show Answer & Explanation

Answer: (c) 18 − 5n

Explanation:
1. a = 13, d = −5. a_n = 13 + (n − 1)(−5) = 18 − 5n.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 9: Which term of the A.P. 84, 80, 76, ... is 0?
(a) 21st
(b) 23rd
(c) 22nd
(d) 20th
Show Answer & Explanation

Answer: (c) 22nd

Explanation:
1. 0 = 84 + (n − 1)(−4) gives n − 1 = 21, so n = 22.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 10: Which term of the A.P. 4, 9, 14, ... is 254?
(a) 50th
(b) 52nd
(c) 49th
(d) 51st
Show Answer & Explanation

Answer: (d) 51st

Explanation:
1. 254 = 4 + (n − 1)5 gives n − 1 = 50, so n = 51.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 11: Is 68 a term of the A.P. 7, 10, 13, ... ?
(a) Yes, it is the 21st term
(b) Yes, it is the 22nd term
(c) No, because (68 − 7)/3 is not an integer
(d) No, because 68 is even
Show Answer & Explanation

Answer: (c) No, because (68 − 7)/3 is not an integer

Explanation:
1. 68 = 7 + (n − 1)3 gives n − 1 = 61/3, which is not a whole number. So 68 is not a term.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 12: Is 302 a term of the A.P. 3, 8, 13, ... ?
(a) Yes, it is the 61st term
(b) Yes, it is the 60th term
(c) No, because 302 is even
(d) No, because (302 − 3)/5 is not an integer
Show Answer & Explanation

Answer: (d) No, because (302 − 3)/5 is not an integer

Explanation:
1. 302 = 3 + (n − 1)5 gives n − 1 = 299/5, which is not an integer. So 302 is not a term.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 13: The number of terms in the A.P. −1, −5/6, −2/3, −1/2, ..., 10/3 is
(a) 26
(b) 28
(c) 25
(d) 27
Show Answer & Explanation

Answer: (d) 27

Explanation:
1. a = −1, d = 1/6. 10/3 = −1 + (n − 1)/6 gives (n − 1)/6 = 13/3, so n − 1 = 26 and n = 27.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 14: The 10th and 18th terms of an A.P. are 41 and 73. Its 26th term is
(a) 101
(b) 109
(c) 105
(d) 97
Show Answer & Explanation

Answer: (c) 105

Explanation:
1. Subtracting, 8d = 32, so d = 4 and a = 41 − 36 = 5. a₂₆ = 5 + 25(4) = 105.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 15: The 6th and 17th terms of an A.P. are 19 and 41. Its 40th term is
(a) 85
(b) 89
(c) 87
(d) 91
Show Answer & Explanation

Answer: (c) 87

Explanation:
1. Subtracting, 11d = 22, so d = 2 and a = 19 − 10 = 9. a₄₀ = 9 + 39(2) = 87.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 16: If 10 times the 10th term of an A.P. equals 15 times its 15th term, then its 25th term is
(a) 1
(b) 0
(c) 25
(d) −1
Show Answer & Explanation

Answer: (b) 0

Explanation:
1. 10(a + 9d) = 15(a + 14d) gives 10a + 90d = 15a + 210d, so −5a = 120d and a = −24d. Then a₂₅ = a + 24d = 0.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 17: The sum of all integers between 84 and 719 which are multiples of 5 is
(a) 50800
(b) 50850
(c) 50750
(d) 51200
Show Answer & Explanation

Answer: (a) 50800

Explanation:
1. The multiples are 85, 90, ..., 715, which is 127 terms. Sum = 127/2 × (85 + 715) = 127 × 400 = 50800.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 18: The sum of all integers between 50 and 500 which are divisible by 7 is
(a) 17640
(b) 17750
(c) 17696
(d) 18000
Show Answer & Explanation

Answer: (c) 17696

Explanation:
1. The numbers are 56, 63, ..., 497, which is 64 terms. Sum = 64/2 × (56 + 497) = 32 × 553 = 17696.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 19: The sum of the first 60 natural numbers is
(a) 1770
(b) 1860
(c) 1830
(d) 3660
Show Answer & Explanation

Answer: (c) 1830

Explanation:
1. S = n(n + 1)/2 = 60 × 61/2 = 1830.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 20: The sum of all two-digit numbers is
(a) 4950
(b) 4905
(c) 4860
(d) 4680
Show Answer & Explanation

Answer: (b) 4905

Explanation:
1. The numbers 10, 11, ..., 99 are 90 terms. Sum = 90/2 × (10 + 99) = 45 × 109 = 4905.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 21: Which term of the A.P. 5, 8, 11, ... is 320?
(a) 105th
(b) 104th
(c) 106th
(d) 107th
Show Answer & Explanation

Answer: (c) 106th

Explanation:
1. 320 = 5 + (n − 1)3 gives n − 1 = 105, so n = 106.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

Question 22: If (k + 1), 3k and (4k + 2) are three consecutive terms of an A.P., then k equals
(a) 3
(b) 0
(c) 1
(d) 2
Show Answer & Explanation

Answer: (a) 3

Explanation:
1. 2(3k) = (k + 1) + (4k + 2) gives 6k = 5k + 3, so k = 3. The terms are 4, 9, 14.

Teacher's Note:
1. Write the standard formulas a_n = a + (n − 1)d and S_n = n/2 [2a + (n − 1)d], form equations from the given data and solve them.
2. Check by listing the first few terms.

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Practice MCQs for Class 10 Mathematics Chapter 05 Arithmetic Progressions

Chapter MCQs with Answers for Class 10 Mathematics

Review structured objective questions for Class 10 Mathematics Chapter 05 Arithmetic Progressions. Built according to official CBSE guidelines, these MCQ sets support daily revision and core concept reinforcement.

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FAQs

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