Question

What is the $9^{th}$ term in the following sequence of natural numbers?
$1,1+3,1+3+5,1+3+5+7,.....$

• A. $9^2$
• B. $2^9$
• C. $9^3$
• D. $3^9$

Answer 1

The correct option is A $9^2$

First, observe the pattern from the given sequence,
$1^{st}$ term = $1=1^2$
$2^{nd}$ term = $1+3=4=2^2$
$3^{rd}$ term= $1+3+5=9=3^2$
$4^{th}$ term =$1+3+5+7=16=4^2$
.
.
.

So, each term is clearly obtained by adding an odd number with the previous term, resulting in a perfect square of that term.

Hence,
$9^{th}$ term = $9^2$