Question

The sum of first 9 terms of an ap is 171 and that for first 24 terms is 96 find the ap

Answer 1

ANSWER:-

Given:

The sum of first 9 terms of an A.P. is 171 & that for first 24 terms of an A.P is 96.

To find:

The A.P.

Explanation:

If a be the first term & d be the common difference of an A.P., then sum of n terms is given by Sn= $\frac{n}{2}$[2a+(n-1)d]

A/q

a9= 171

⇒ 171= $\frac{9}{2}$[2a+(9-1)d]

⇒ 19= $\frac{1}{2}$[2a+8d]

⇒ 2a+8d= 38..............(1)

&

It is also given that sum of first 24 terms is 96.

a24= 96

⇒ 96= $\frac{24}{2}$[2a+(24-1)d]

⇒ 96= 12[2a+23d]

⇒ 2a+23d= 8.................(2)

∴ Subtracting equation (1) from (2), we get;

2a+23d=8

2a+8d=38

(-)   (-)    (-)

__________

⇒ 15d= -30

⇒ d= $\frac{-30}{15}$

⇒ d= -2

Putting the value of d in equation (1), we get;

⇒ 2a+8d= 38

⇒ 2a+ 8(-2)=38

⇒ 2a +(-16)=38

⇒ 2a- 16=38

⇒ 2a= 38 +16

⇒ 2a= 54

⇒ a= 54/2

⇒ a= 27

Thus,

The A.P. is 27, 25, 23, 21.........