Question

The 5^th, 8^th and 11^th terms of a GP are a, b, c respectively. Show that b² = ac

Answer 1

It is given in the question that 5^th, 8^th and 11^th terms of GP are a, b and c respectively. Let us assume the GP is A, AR, AR² , and AR³…. 

So, the n^th term of this GP is an = AR^n-1

Now, 5^th term, a₅ = AR⁴ = a ...... (1)

8^th term, a₈ = AR⁷ = b ...... (2)

11^th term, a₁₁ = AR¹⁰ = c ...... (3)

Dividing equation (3) by (2) and (2) by (1),

So, both equation (4) and (5) gives the value of R3 . So we can equate them.

\(\frac{c}{b} = \frac{b}{a}\) = R³

∴ b² = ac

Hence proved.