Question

The common difference of an arithmetic progression in which a15 -a6 =-27/2 ,is ( where an is the nth term of the given AP)

Answer 1

Let A be the first term and D be the common difference.

It is given that ,$a_{15} - a_{6}$ = -27/2

Using the formula of nth term of an A.P, having A as the first term and D as the common difference

→$a_{n}$=  A + (n-1) D

→A + (15-1) D - [A + (6-1) D] = -27/2

→A + 14 D - A - 5 D=-27/2

→ 9 D=-27/2

Dividing  both sides by 9, we get

D= - 3/2= Common Difference