Thursday, February 16, 2017

The sum of first 15 terms of an A.P. is 105 and the sum of next 15 terms is 780. Find the A. P.

For an AP
with first term a and the common difference d, the sum of the first n terms is given as (2a +
(n-1)d)(n/2).

Now for the AP given the sum of the first 15 terms is
105

=> (2a + 14d)(15/2) = 105...(1)

The sum of the next
15 terms is the sum of the first 15 terms subtracted from the sum of the first 30
terms.

=> (2a + 29d)(30/2) - 105 = 780

=> (2a + 29d)
= 885/15

=> (2a + 29d) = 59

(1)


=> (2a + 14d)(15/2) = 105

=> 2a + 14d = 14


2a + 29d - 2a - 14d = 59 - 14

=> 15d = 45


=> d = 3

2a + 14d = 14

=> 2a = 14 -
42

=> 2a = -28

=> a = -14


Therefore the AP has the first term as -14 and the common difference is
3.

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