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

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Formulae for Arithmetic Series

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