NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 8

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.