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

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

oobleck · Answer

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...