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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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