Question

Find the sum of the following AP: 1, 3, 5, 7 …199.

• A. 10000
• B. 12000
• C. 13333
• D. 20000

Answer 1

The correct option is A 10000

Let, the first term be $a$, common difference be $d$ and the last term be $l$.

$Given,a=1,d=2,a_n=l=199a+(n-1)d=199$
$1+(n-1)2=199$
$\Rightarrow 1+2n-2=199$
$\Rightarrow 2n=200$
$n=100$

The sum of A.P is given as : $S_n=\frac{n}{2}(a+l)$
So, $S_n=\frac{100}{2}(1+199)$
$S_n=10000$