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The sum of the first n terms of an AP is $5 n 2 2 + 3 n 2$ . Which is the nth term and the 20th term of this AP?

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n t h term is [4 + (n − 1)]

and 20th term is 23

n t h term is [4 + (n + 1)]

and 20th term is 25

n t h term is [4 − (n − 1)]

and 20th term is 27

n t h term is [4 (n − 1)]

and 20th term is 20

answer is A.

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Detailed Solution

Given:

S n = 5 n 2 2 + 3 n 2 … … . (1)

Determining the sum of the first term by putting n=1 in equation (1).
Therefore, the sum of the 1st term:

= 512 + 312 = 5 + 3 2 = 82 = 4

Determining the sum of the first two terms by putting n=2 equation (1).
Therefore, the sum of the first two terms:

= 542 + 322 = 5 × 2 + 3 = 10 + 3 = 13

So,

2 n d Term = sum of first 2 terms − Sum of first term

⇒

13 - 4 = 9
Determining the common difference for the given AP:

∴ d = 9 - 4

d = 5
Therefore,

n t h term

a n = 4 + n − 1 − − − (2)

Put n = 20 in equation (2) to determining the 20

t h

term of AP.

∴ a 20 = 4 + (20 − 1)

⇒ a 20 = 4 + 19 ⇒ a 20 = 23

Therefore the

n t h

term and 20th terms of A.P. are

4 + (n − 1)

and 23 respectively.
Hence, option (1) is correct.

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