NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 5

Download PDF of This Page (Size: 387K)

Formula for the nth term of a Geometric Sequence

Formula for the Nth Term of a Geometric Sequence

Formula for the nth term of a Geometric Sequence

1. The first term of a G.P. is . The sum of the third term and fifth term is . Find the common ratio of G.P.

Answer:

Consider be the first term and the common ratio of the G.P. respectively.

(Taking real roots)

So, the common ratio of the G.P. is .

2. The sum of three numbers in G.P. is . If we subtract from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

Answer:

Consider the three numbers in G.P. be .

From the given condition,

……………………….… (1)

forms an A.P.

……………………………… (2)

From (1) and (2), we get

When

Therefore, when , the three numbers in G.P. are .

When, , the three numbers in G.P. are .

So, in either case, the three required numbers are .