Question

find the common difference of an AP whose first term is 1 and the sum of the next four terms is one-third to the sum of the next four terms

Answer 1

Given, a=1
and,
a1 +a2+a3+a4 = 1/3 ( a5+a6+a7+a8 )

4a + 10d = 1/3 ( 4a + 26d )
12a + 30d = 4a +26d
8a = -4d
Hence a=1

d = -8/4

d = 2