Question

Without formal addition, find the sum of $1+3+5+7+9+11+13+15.$

• A. $46$
• B. $64$
• C. $36$
• D. $49$

Answer 1

The correct option is B $64$

$\underset{–}{\text{Need to find:}}$ Value of $1+3+5+7+9+11+13+15$ without formal addition

$\bullet$ Sum of first $\underset{–}{2\text{odd terms}}$ $=1+3=4=\underset{–}{2^2}$
$\bullet$ Sum of first $\underset{–}{3\text{odd terms}}$ $=1+3+5=9=\underset{–}{3^2}$
$\bullet$ Sum of first $\underset{–}{4\text{odd terms}}$ $=1+3+5+7=16=\underset{–}{4^2}$
$.$
$.$
$.$

Hence, we can conclude:

Sum of first $n$ odd numbers equals to $n^2.$

$\therefore 1+3+5+7+9+11+13+15=$ Sum of first $\underset{–}{8}$ odd numbers $=\underset{–}{8^2=64}$

Hence, the value of the sum $1+3+5+7+9+11+13+15$ would be equal to $64$.

Therefore, option (b.) is the correct answer.