Asked by sana
the ratio of the sum to terms p and q terms of an a.p. is psquare:qsquare. prove that the common difference of the a.p. is twice the first term
Answers
Answered by
Steve
p/2 (2a+(p-1)d)
------------------- = p^2/q^2
q/2 (2a+(q-1)d)
2a+pd-d
---------- = p/q
2a+qd-d
q(2a+pd-d) = p(2a+qd-d)
pqd + q(2a-d) = pqd + p(2a-d)
(p-q)(2a-d) = 0
So, either p=q or d=2a
------------------- = p^2/q^2
q/2 (2a+(q-1)d)
2a+pd-d
---------- = p/q
2a+qd-d
q(2a+pd-d) = p(2a+qd-d)
pqd + q(2a-d) = pqd + p(2a-d)
(p-q)(2a-d) = 0
So, either p=q or d=2a
There are no AI answers yet. The ability to request AI answers is coming soon!