NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. If f is a function satisfying . for all , such that

, find the value of .

Answer:

It is given that,

for all … eq (1)

Taking in (1) ,

we obtain

Similarly,

forms a G. P. with both the first term and common ratio equal to

It is known that ,

It is given that,

So, the value of is .

2. The sum of some terms of G. P. is whose first term and the common ratio are , respectively. Find the last term and the number of terms.

Answer:

Consider the sum of n terms of the G. P. be .

It is known that,

It is given that the first term a is and common ratio

Last term of the G. P term

Thus, the last term of the G. P. is .