Mathematics - Sequence & Series Question with Solution | TestHub

Let $a_{1,}{a}_1+d_{1,}{a}_1+2d.................$first $A.P.$

$a_{40}=a_1+39d=-159$.....................(1)

$a_{100}=a_1+99d=-399$....................(2)

$d=-4,a_1=-3$

now

$b_{100}=a_{70}$

$\Rightarrow b_1+99D=a_1+69d$

$b_1+99(-2)=-3+69(-4)$

($\because$Accoding to question $D=d+2$)

$\Rightarrow b_1=-81$