Sequence & Series Level-3 Quiz-3

1. Each question is followed by two statements, I and II. Answer each question based on the following directions:

What is the sum of the first 25 terms of an arithmetic progression?
I. The first term of the progression is 3.
II. The sum of the first 10 terms of the progression is equal to the sum of the first 15 terms of the progression.

If the question can be answered by using one of
the statements alone, but cannot be answered
by using the other statement alone

If the question can be answered by using either
statement alone.

If the question can be answered by using both
the statements together, but cannot be answered
by using either statement alone.

If the question cannot be answered even by using
both the statements together.

Find the value of x+y+z if 1, x, y, z, 16 are in G.P.

3. Find the sum to n terms of the series 8 + 88 + 888 + …

(10^n -1)-8n/9

80/81 (10^n -1)-8n/9

81/80 (10^n -1)-8n/9

None

4. Find the value of n, if the sum to n terms of a geometric series is 4488 3/4 . The first term and the common ratio of the series are 216 and 3/2, respectively.

5. A group of 810 children arranged themselves in N rows for a group photograph. In each row, there were three more children than the row behind. Which of the following can be the value of N?

6. Find the sum up to 25 terms of the series 1/2 + 3/4 + 7/8 + 15/16 + …

24.2 ^25 +1 / 2^25

24.2 ^24 +1 / 2^25

24.2 ^25 +1 / 2^23

None of these

7. Find the value of (100 × 1) + (99 × 2) + (98 × 3) + … + (2 × 99) + (1 × 100).

171700

173900

145600

None of these

8. Find the sum of the series p (p + q) + p^2 (p^2 + q^2) + p^3(p^3 + q^3) + …up to infinite terms if −1 < p <1 and −1 < q < 1.

P^2 – 2p^3q+pq / (1-p^2)(1-pq)

P^2 – p^3q+pq / (1-p^2)(1-pq)

P^2 – 2p^2q+pq / (1-p^3)(1-pq)

2P^2 – 2p^3q+pq / (1-p^2)(1-pq)

9. Find the sum of the first 20 terms of the following series 1^2 (3) + 2^2 (4) + 3^2 (5) + 4^2 (6) +…

49840

38368

42360

11240

10. Find the value of 1(3^2-2^2) + 1/(7^2-2^2) + …..1/(39^2-2^2)

5/41

10/41

18/37

31/41

Sequence & Series Level-3 Quiz-3

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