Question

find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.

Answer 1

common difference is -30

Answer 2

Given,

$S_{4} = 1/2 [ S_{8} - S_{4} ]$
=> $3/2S_{4} = 1/2S_{8}$
=> $3S_{4} = S_{8}$
=> 3 * 4/2 ( 2a + (4-1)d ) =  8/2 ( 2a + (8-1)d )
=> 3 * 2 ( 2a + 3d ) = 4 ( 2a + 7d )
=> 6a + 9d = 4a + 14d
=> 2a - 5d = 0
=> 2a = 5d

Now, a = -5; 
=> -10 = 5d
=> d = -2 ........