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

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.