Question

The third term of a gp is 2. Calculate the product of the first 5 terms.

Answer 1

Step-by-step explanation:

ar^(n-1)

Given, ar^(3-1) = 2

ar^2 = 2 a = 2/r^2 --- (1)

Assuming r >1

Sn = a(r^n - 1)/ (r - 1)

S5 = a(r^4-1)/(r-1)

= 2/r^2(r^2 + 1)(r^2 - 1)/(r - 1)

= 2/r^2[r^2 + 1](r-1)(r+1)/(r-1)

= 2/r^2(r^2 + 1)(r + 1)

= [2(r^3 + r^2 + r + 1)]/r^2