CA Foundation P3 · Chapter 6

Sequence and Series - Arithmetic and Geometric Progressions MCQs with Answers

9 multiple-choice questions on Sequence and Series - Arithmetic and Geometric Progressions for CA Foundation P3 Quantitative Aptitude. Try each one before revealing the answer and explanation.

1. Question 1

   The 15th term of the A.P. 7, 11, 15, 19, ... is:

   • A) 67
   • B) 59
   • C) 60
   • D) 63
   Show answer & explanation

   Answer: D) 63

   tₙ = a + (n − 1)d with a = 7 and d = 4. t₁₅ = 7 + 14 x 4 = 63. Using n instead of n − 1 gives 7 + 60 = 67.

2. Question 2

   The sum of the first 20 terms of the A.P. 3, 8, 13, ... is:

   • A) 1010
   • B) 1060
   • C) 98
   • D) 505
   Show answer & explanation

   Answer: A) 1010

   Sₙ = n/2 [2a + (n − 1)d] = 20/2 x [6 + 19 x 5] = 10 x 101 = 1,010. Using 20 instead of 19 gives 10 x 106 = 1,060, and 98 is the 20th term.

3. Question 3

   How many terms of the A.P. 5, 9, 13, ... must be taken so that their sum is 230?

   • A) 9
   • B) 11
   • C) 10
   • D) 23
   Show answer & explanation

   Answer: C) 10

   Sₙ = n/2 [10 + 4(n − 1)] = n(2n + 3) = 230. So 2n² + 3n − 230 = 0, giving n = [−3 + √(9 + 1840)]/4 = (−3 + 43)/4 = 10. Check: 10 x 23 = 230.

4. Question 4

   The 8th term of the G.P. 3, 6, 12, 24, ... is:

   • A) 768
   • B) 192
   • C) 48
   • D) 384
   Show answer & explanation

   Answer: D) 384

   tₙ = arⁿ⁻¹ with a = 3, r = 2. t₈ = 3 x 2⁷ = 3 x 128 = 384. Using 2⁸ gives 768 and 2⁶ gives 192.

5. Question 5

   The sum to infinity of the G.P. 12, 4, 4/3, ... is:

   • A) 16
   • B) 18
   • C) 36
   • D) 9
   Show answer & explanation

   Answer: B) 18

   Here a = 12 and r = 1/3, with |r| < 1. S∞ = a/(1 − r) = 12/(2/3) = 18. Dividing by r instead of (1 − r) gives 36.

6. Question 6

   The sum of the first 6 terms of the G.P. 2, 6, 18, ... is:

   • A) 1458
   • B) 486
   • C) 728
   • D) 364
   Show answer & explanation

   Answer: C) 728

   a = 2, r = 3. S₆ = a(rⁿ − 1)/(r − 1) = 2(3⁶ − 1)/2 = 729 − 1 = 728. 486 is the 6th term, and 364 forgets that the factor a = 2 cancels with (r − 1) = 2.

7. Question 7

   Three numbers in A.P. have sum 27 and product 504. The largest of the numbers is:

   • A) 14
   • B) 12
   • C) 13
   • D) 16
   Show answer & explanation

   Answer: A) 14

   Let the numbers be a − d, a, a + d. Sum 3a = 27 gives a = 9. Product 9(81 − d²) = 504, so 81 − d² = 56 and d = 5. The numbers are 4, 9, 14 and the largest is 14.

8. Question 8

   The arithmetic mean and geometric mean of two positive numbers are 25 and 15 respectively. The numbers are:

   • A) 45 and 5
   • B) 40 and 10
   • C) 30 and 20
   • D) 35 and 15
   Show answer & explanation

   Answer: A) 45 and 5

   Sum = 2 x 25 = 50 and product = 15² = 225. The numbers are roots of x² − 50x + 225 = 0, i.e. (x − 45)(x − 5) = 0, so 45 and 5. 40 and 10 have AM 25 but GM 20.

9. Question 9

   The sum of the first n terms of the series 0.7 + 0.77 + 0.777 + ... is:

   • A) (7/9)(n − 1 + 10⁻ⁿ)
   • B) (7/81)(9n + 1 − 10⁻ⁿ)
   • C) (7/9)(9n − 1 + 10⁻ⁿ)
   • D) (7/81)(9n − 1 + 10⁻ⁿ)
   Show answer & explanation

   Answer: D) (7/81)(9n − 1 + 10⁻ⁿ)

   Write S = (7/9)[0.9 + 0.99 + 0.999 + ...] = (7/9)[(1 − 0.1) + (1 − 0.01) + ...] = (7/9)[n − (0.1)(1 − 10⁻ⁿ)/0.9] = (7/9)[n − (1 − 10⁻ⁿ)/9] = (7/81)(9n − 1 + 10⁻ⁿ). Check n = 2: (7/81)(17.01) = 1.47 = 0.7 + 0.77.