Question

First consecutive terms of G.P are equal to three consecutive terms of an A.P if the sum of the first seven terms of A.P is -14 calculate common difference first term of A.P common ratio first term of G.P

Answer 1

If the two sequences have the same first term, then
7/2 (2a+6d) = -14
ar = a+d
ar^2 = a+2d
This leads to the trivial sequence -2,-2,-2,-2,-2,-2,-2
where d=0 and r=1

If the terms of the AP start with b, and the kth, k+1st, k+2nd terms match, then
7/2 (2b+6d) = -14
a = b+(k-1)d
ar = b+kd
ar^2 = b+(k+1)d
I get the same trivial sequences.
Hmmmm...