Show that the products of the corresponding terms of the sequences a, ar, ar², …ar^n-1 and A, AR, AR², … AR^n-1 form a G.P, and find the common ratio

Solution:

The given sequences are a, ar, ar², .... ar^{n - 1} and A, AR, AR², AR^{n - 1}

We need to prove that the sequence: aA, arAR, ar²AR², ....., ar^n-1AR^n-1 form a G.P.

Let us find the ratio of the sequence

⇒ a₂ / a₁ = arAR / aA

= rR

⇒ a₃ / a₂ = ar²AR² / arAR

= rR

Thus, the above sequence forms a G.P with a common ratio rR

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 20

Show that the products of the corresponding terms of the sequences a, ar, ar², .... ar^{n - 1} and A, AR, AR², AR^{n - 1} form a G.P and find the common ratio.

Summary:

We had to find the common ratio and prove that the products of the corresponding terms of the sequences a, ar, ar², .... ar^{n - 1} and A, AR, AR², AR^{n - 1} which we have proved