Question

Q.12

Answer 1

`"Sum of first 10 terms" = -80`

`⇒ 10/2[2a+(10-1)d]=-80`

`⇒5[2a+9d]=-80`

`⇒2a+9d=-16............(1)`

And, sum of next 10 term =-280

`"⇒ Sum of first 20 terms= sun of first ten terms +sun of nect 10 terms "`

                                      `=-80+(-280)`

                                   `  =-360`

`⇒20/2[2a+(20-1)d]=-360`

`⇒10[2a+19d0=-360]`

`⇒ 2a+19d=-36 .............(2)`

Substracting (1) from (2), we get 

`10d=-20⇒ d=-2`

`⇒2a+9xx(-2)=-16`

`⇒2a-18=-16`

`⇒2a=2⇒a=1`

∴ Required A.P = `a,a++d, a+2d, a+3d,..........`

                       ` = 1,-1,-3,-5,..................`