Question:
The sum of the first k terms of a series is 3k2 + 5k. Which one of the following is correct?
The sum of the first k terms of a series is 3k2 + 5k. Which one of the following is correct?
Options:
- a) The terms of S form an arithmetic progression with common difference 14.
- b) The terms of S form an arithmetic progression with common difference 6.
- c) The terms of S form a geometric progression with a common ratio 10 7 .
- d) The terms of S form a geometric progression with a common ratio 11 4 .
- a) The terms of S form an arithmetic progression with common difference 14.
- b) The terms of S form an arithmetic progression with common difference 6.
- c) The terms of S form a geometric progression with a common ratio 10 7 .
- d) The terms of S form a geometric progression with a common ratio 11 4 .
correct answer : b)
Explanation:
Sk = 3k2 + 5k
S1 = 3 + 5 = 8
S2 = 12 + 10 = 22
S3 = 27 + 15 = 42
a1 = S1 = 8
a2 = S2 – S1 = 22 – 8 = 14
Solved Paper – 2025 (I)
a3 = S3 – S2 = 42 – 22 = 20
\ Series = 8 + 14 + 20 ….. are in A.P . with
common difference = 14 – 8 = 6.
Sk = 3k2 + 5k
S1 = 3 + 5 = 8
S2 = 12 + 10 = 22
S3 = 27 + 15 = 42
a1 = S1 = 8
a2 = S2 – S1 = 22 – 8 = 14
Solved Paper – 2025 (I)
a3 = S3 – S2 = 42 – 22 = 20
\ Series = 8 + 14 + 20 ….. are in A.P . with
common difference = 14 – 8 = 6.