find the following:

Question

Let a1,a2,a3.............  be terms of an AP. If (a1+a2+a3+a4...............ap)/(a1+a2+a3+a4................aq)=p^2/Q^2, THEN find the value of a6/a21.

Comments

@Rahul, Please correct your question in p^2/Q^2

Answer 1

Your question is a bit not clear.But what I understand showing you.

Given  a1,a2,a3.............  be terms of an AP

Let common difference is d

(a1+a2+a3+a4...............ap)/(a1+a2+a3+a4................aq)=p^2/Q^2

p/2[2a₁ + (p-1)d] / q/2[2a₁+(q-1)d] = P²/Q²

^=> p[2a₁ + (p-1)d] / q[2a₁+(q-1)d] = P²/Q²  --------------------(1)

Now a6/a21 = a₁ + (6-1)d / a₁ + (21-1)d

=> a₆/a₂₁ = a₁ + 5d / a₁ + 20d  -------------(2)

Now find the ratio using equation (1) and (2)