Question

Find the sum of terms 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

The formula to find the $n^{th}$ term of an arithmetic progression is $t_n=a+(n-1)d$.

where,

'$a$' is the first term,

'd' is the common difference,

'n' is the no. of terms,

'$t_n$' is the $n^{th}$ term.

Given,

first term, a=1,

common difference, d =2,

$n^{th}term{t}_n=199$
$t_n=a+(n-1)d=199$
$\Rightarrow$$1+(n-1)2=199$
$\Rightarrow 1+2n-2=199$
$\Rightarrow 2n=200$
$\Rightarrow$$n=100$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

where $S_n$ is the sum of n terms of the AP.

Substituting the values of a, d and n, we get

$S_n=\frac{100}{2}\left[2\right(1)+(100-1\left)2\right]$

$S_n=\frac{100}{2}(1+199)$
$S_n=10000$