In an A P , the ratio of the sum of the first p terms to the sum of the first q terms is p^2: q^2 . Which one of the following is correct?

Step-by-step solution

We have, aligned & S_p S_q = p^2 q^2 & p 2 [2 a+(p-1) d] q 2 [2 a+(q-1) d] = p^2 q^2 S_n= n 2 [2 a+(n-1) d] & 2 a+(p-1) d 2 a+(q-1) d = p q & 2 a q+q(p-1) d=2 a p+p(q-1) d & 2 a(q-p)=d(q-p) & 2 a=d or d=2 a aligned This, the common difference is equal to twice of the first term.