Question

The 5th , 8 th, and 9th term of a. GP are P, q, and S. Respectively . Prove that q square = ps

Answer 1

We know that  an = ar^n-1

The fifth term a5 = a r^5-1 = ar^4 = p ------------  ( 1 )

The 8th term a8 = a r^8-1 = ar^7 = q ------------- ( 2 )

The 11th term a11 = a r^11-1 = ar^10 = s ----------- ( 3 )

On solving (2) and (1), we get

ar^7/ar^4 = q/p

r^3 = q/p     ------------------ (4)

On solving (3) and (2), we get

 ar^10/ar^7 = s/q 

 r^3 = s/q          ----------------- (5)

On solving (4) and (5), we get

q/p = s/q

q^2 = ps.

Hope this helps!