Question

The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.

Answer 1

Solution:

Given sum of 5th term and 9th term of AP=30
$a+4d+a+8d=3$

$2a+12d=30$ ---Equation (1)

Given that 25 term is three times of 3rd term in AP

25th term= 3 (8th term)

$(a+24d)=3(a+7d)$

$a+24d=3a+21d$

$24d-21d=3a-a$

$3d=2a$ --- equation 2

Substitute the value of $2a$ in equation (1) we get

$2a+12d=30$

$3d+12d=30$

$15d=30$

$d=2$

Therefore,

$2a=3d$

$2a=3\times 2$

$a=3$

Therefore, AP is $3,5,7,\mathrm{9...}$