NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 .