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

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Formulae for Arithmetic Series

Formulae for Arithmetic Series

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