Question

In a GP the sum of the second and the third term is 6 and the sum of the third and fourth is -12.Find the first term and common difference

Answer 1

GP's have a common ratio, not a common differece.
ar + ar^2 = 6
ar^2 + ar^3 = -12

ar(1+r) = 6
ar^2 (1+r) = -12
divide and you have
r = -2
so a = 3
The GP is 3,-6,12,-24,...