NCERT Class 11 Mathematics Solutions: Chapter 9 – Sequences and Series Miscellaneous Exercise 9 Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Arithmetic and Geometric Sequence and Series

1. The terms of an A. P. are respectively. Show that

Answer:

Consider be the first term and the common difference of the A. P. respectively.

The nth term of an A. P. is given by,

So,

… eq (1)

… eq (2)

… eq (3)

Subtracting equation (2) from (1) , we obtain

… eq (4)

Subtracting equation (3) from (2) , we obtain

… eq (5)

Equating both the values of d obtained in (4) and (5) ,

(By rearranging terms)

So, the given result is proved.

2. If are in A. P. , prove that are A. P.

Answer:

It is given that are in A. P.

So, are in A. P.