Question

Find the sum of the first $29$ positive odd number.

• A. $820$
• B. $811$
• C. $841$
• D. $821$

Answer 1

The correct option is C $841$

First $29$ odd integers in AP form $=1,3,5,7,.......$

The sum of $n$ terms of an arithmetic sequence can be calculated by $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
Where, $n$ denotes the total number of terms.
$a=$first term
$d=$common difference
$S_n$ = Sum of n terms

For this case,

$a=1$
$n=29$

$d=3-1=5-3=2$

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

$=\frac{29}{2}[2+(29-1\left)2\right)]$

$=841$ (Ans $\to$ C)