Question

In an A.P. of 99 terms, the sum of all odd numbered terms is 5100. Find the sum of all the even numbered terms.

• A. 5100
• B. 4998
• C. 5048
• D. 5198

Answer 1

The correct option is B 4998

Let the first term and common difference of the A.P be a and d respectively.

Sum of A.P of first n terms $=\frac{n}{2}[firstterm+lastterm]$

Let the terms of the A.P be a, a+d, a+2d, ..., a+98d

Odd numbered terms
$1^{st}term,3^{rd}term,...,{99}^{th}term$
a, a+2d, a+4d, ..., a+98d

Even numbered terms
$2^{nd}term,4^{th}term,...,{98}^{th}term$
a+d, a+3d, a+5d, ..., a+97d

Sum of odd numbered terms $=\frac{50}{2}[a+a+98d]=50a+2450d$

Sum of even numbered terms $=\frac{49}{2}[a+d+a+97d]=49a+2401d$

Sum of odd numbered terms is given as 5100.

$\Rightarrow 50a+2450d=5100\to a+49d=102$

Sum of even numbered terms $=49a+2401d=49[a+49d]=49\times 102=4998$