NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 4

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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 .