Question

Q.6

Answer 1

The sum of the `4^th` end the `8^th` terns of an A.P. is 24 and the sum of the sixth term and the tenth is 44.

find the first three terms of the A.P

Given, 

`t_4+t_8=24`

`⇒ (a+3d)+(a+7d)=24`

`⇒2a+10d=24`

`⇒a+5d=12 ..........(1)`

And, 

`t_6+t_10=44`

`⇒(a+5d)+(a+9d)=44`

`⇒2a+14d=144`

`⇒a+7d=22...................(2)`

Substituting value of d in (1) fro (2), we get 

`a+5xx5=12`

`⇒a+25=12`

`⇒a=-13=1^(st) "term"`

`a+d=-13+5=-8=2^(nd) "term"`

`a+2d=-13+2xx5=-13+10=-3=3^(rd) "term"`

`"Hence, the first three terms of an A.P.  are "-13,-8 and -5.`