NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 11 (For CBSE, ICSE, IAS, NET, NRA 2023)
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1. If are in A. P; b, c, d are in G. P and are in A. P. prove are in G. P.
Answer:
It is given that are in A. P.
… eq (1)
It is given that are in G. P.
… eq (2)
Also, are in A. P.
… eq (3)
It has to be proved that are in G. P.
i.e.. ,
From (1)
From (2)
Substituting these values in eq (3)
So, are G. P.
2. Find the sum of the following series up to terms:
(i)
(ii)
Answer: (i)
Consider terms
Answer: (ii)
Consider terms