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

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Sum of a Geometric Series

1. If are in G. P, prove that are in G. P.

Answer:

It is given that are in G. P.

… eq (1)

… eq (2)

… eq (3)

It has to be proved that are in G. P.

i.e.

Consider L. H. S.

[Using (1) and (2) ]

[Using (3) ]

Thus, are in G. P.

2. If a and b are the roots of are roots of , where , form a G. P.

Prove that .

Answer:

It is given that a and b are the roots of

… eq (1)

Also, are the roots of

… eq (2)

It is given that are in G. P.

Consider From (1) and (2) , we obtain

On dividing, we obtain

When

When

Case I:

When ,

i.e.. ,

Case II

When ,

i.e.. ,

Thus, in both the cases, we obtain