Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms, the first term being 12.

Answer 1

You have:

S3 = 1/2 (S7-S3)
3/2 (24+2d) = 1/2 (7/2 (24+6d) - 3/2 (24+2d))

d = 2

AP = 12,14,16, 18,20,22,24

I'll let you verify the result.