# Show that the products of the corresponding terms of the sequences a, ar, ar^{2}, …ar^{n-1} and A, AR, AR^{2}, … AR^{n-1} form a G.P, and find the common ratio

**Solution:**

The given sequences are a, ar, ar^{2}, .... ar^{n }^{- }^{1} and A, AR, AR^{2}, AR^{n }^{- 1}

We need to prove that the sequence: aA, arAR, ar^{2}AR^{2}, ....., ar^{n}^{-1}AR^{n}^{-1} form a G.P.

Let us find the ratio of the sequence

⇒ a_{2 }/ a_{1} = arAR / aA

= rR

⇒ a_{3 }/ a_{2} = ar^{2}AR^{2 }/ 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, ar^{2}, .... ar^{n }^{- }^{1} and A, AR, AR^{2}, 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, ar^{2}, .... ar^{n }^{- }^{1} and A, AR, AR^{2}, AR^{n }^{- }^{1} which we have proved