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State True/False.

If the sum of the first 14 terms of an AP is 1505 and the first term of an AP is 10, then 25th term is 370.

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True

False

answer is A.

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Detailed Solution

Given that the sum of 14 term is 1505.

⇒ S 14 = 1505

Let the first term be a and common difference be d.
a = 10
Formula used for sum of first n term of A.P.:

S n = n 2 [2 a + (n − 1) d]

Applying formula for sum of first n terms of A.P.:

∴ S 14 = 142 [2 (10) + (14 − 1) d] ⇒ 1505 = 7 [20 + (13) d] ⇒ 215 = 20 + 13 d ⇒ 13 d = 195 ⇒ d = 15

Therefore, the common difference is 15.
Formula for the

n t h

term:

a n = a + n − 1 × d

So, the 25th term of the A.P. is:

∴ a 25 = 10 + (25 − 1) 15 ⇒ a 25 = 10 + (24) 15 = 10 + 360 = 370

Therefore,

25 th term of the A .P . is 370 .

Thus, the given statement is true.
Hence, option (1) is correct.

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