Question

Let $a_1,a_2,\dots$ and $b_1,b_2,\dots$ be arithmetic progression such that $a_1=25,b_1=75$ and $a_{100}+b_{100}=100,$ then the sum of first hundred term of the progression $a_1+b_1,a_2+b_2$, $\dots$ is equal to

• A. 1000
• B. 100000
• C. 10000
• D. 24000

Answer 1

Answer: (C)

$\left(a_{100}+b_{100}\right)-\left(a_1+b_1\right)=99d\Rightarrow d=0$
$\therefore$Sum of series$=(100/2)\left(a_{100}+b_{100}+a_1+b_1\right)$
$=50(100+100)=10000$