Question

Q.12

Answer 1

${\displaystyle \text{Sum of first 10 terms}=-80}$

${\displaystyle \Rightarrow \frac{10}{2}[2a+(10-1)d]=-80}$

${\displaystyle \Rightarrow 5[2a+9d]=-80}$

${\displaystyle \Rightarrow 2a+9d=-16............\left(1\right)}$

And, sum of next 10 term =-280

${\displaystyle \text{⇒ Sum of first 20 terms= sun of first ten terms +sun of nect 10 terms}}$

                                      ${\displaystyle =-80+(-280)}$

                                   ${\displaystyle =-360}$

${\displaystyle \Rightarrow \frac{20}{2}[2a+(20-1)d]=-360}$

${\displaystyle \Rightarrow 10[2a+19d0=-360]}$

${\displaystyle \Rightarrow 2a+19d=-36.............\left(2\right)}$

Substracting (1) from (2), we get 

${\displaystyle 10d=-20\Rightarrow d=-2}$

${\displaystyle \Rightarrow 2a+9\times (-2)=-16}$

${\displaystyle \Rightarrow 2a-18=-16}$

${\displaystyle \Rightarrow 2a=2\Rightarrow a=1}$

∴ Required A.P = ${\displaystyle a,a++d,a+2d,a+3d,..........}$

                       ${\displaystyle =1,-1,-3,-5,..................}$