Question

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please help in the above attachment..

Answer 1

hello sista @Nidhra nair, pls refer attachment

Answer 2

Given,

First term of GP is a.

nth term of the GP = ar^n - 1 = b. ---------------- (1)

Given that P is the product of n terms.

⇒ P = (a)(ar)(ar^2)(ar)^3...(ar^n - 1)

      = (a * a * a * ...) * (r * r^2 * r^3.... r^n - 1)

      = a^n r^(1 + 2 + 3 +.....(n - 1))

We know that sum of n terms of an AP : sn = (n/2)[2a + (n - 1) * d]

      = a^n (n - 1)/2[2 + (n - 1 - 1) * 1]

      = a^n (n - 1)/2[2 + n - 2]

      = a^n (n - 1)/2[n]

      = a^n r^[n(n - 1)/2]

LHS:

⇒ p^2 = a^2n [r^n(n - 1)]

          = [a^2 r^(n - 1)]^n

          = a[ar^(n - 1)]^n

          = [ab]^n

Hope it helps!