Question

Let $a_1,a$ and $b_1,b_2,....$ be the arithmetic progressions such that $a_1=25,b_1=75$ and $a_{1}00+b_{100}$. The sum of the first one hundred terms of the progressions $(a_1+b_1),(a_2+b_2)$, ...... is _______.

• A. 0
• B. 100
• C. 10, 000
• D. 5, 05, 000

Answer 1

The correct option is C 10, 000

Given there are two A.P's

$a_1,a_2,....and{b}_1,b_2,b_3....$

Also given that $a_1=25and{b}_1=75$

And the sum of $100$th term of both the A.P is $a_{100}+b_{100}=100$

Given a new A.P:

$(a_1+b_1),(a_2+b_2),(a_3+b_3)......(a_{100}+b_{100})$

$\therefore a_1+b_1=25+75=100$

And the last term is $a_{100}+b_{100}=100$

$\therefore S_n=\frac{n}{2}\times (firstterm+lastterm)=50\times (100+100)=10000$