The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that b2 = ac
It is given in the question that 5th, 8th and 11th terms of GP are a, b and c respectively.
Let us assume the GP is A, AR, AR2, and AR3….
So, the nth term of this GP is an = ARn-1
Now, 5th term, a5 = AR4 = a → (1)
8th term, a8 = AR7 = b → (2)
11th term, a11 = AR10 = c → (3)
Dividing equation (3) by (2) and (2) by (1),
→ (4)
→ (5)
So, both equation (4) and (5) gives the value of R3. So we can equate them.
,
∴ b2 = ac,
Hence proved.