Question

Find the sum of the first $15$ positive odd numbers.

• A. $225$
• B. $200$
• C. $210$
• D. $217$

Answer 1

The correct option is A $225$

First $15$ positive odd numbers will be,

$1,3,5,7,9,\dots$

We can observe that these numbers are in A.P.

The sum of first $n$ terms of an A.P whose first term is $a$ and common difference is $d$ can be written as, $S_n=\frac{n}{2}[2a+(n-1\left)d\right].$

From the series of first positive odd numbers we can conclude that, $a=1$ and $d=2.$

Substitute the values of $a,d$ and $n$ in the formula of sum of first $n$ terms of an A.P,

$\begin{array}{cc}{S}_{15}& =\frac{15}{2}[2\times 1+(15-1\left)2\right]\\ & =7.5[2+14\times 2]\\ & =7.5[2+28]\\ & =7.5\left[30\right]\\ & =225\end{array}$

So, the sum of the first $15$ positive odd numbers of the A.P. is $225.$