Question

Find the algebraic expression for the $n^{th}$ term of the pattern given below.
3, 9, 19, 33.....

• A. $2(n^2+1)$
• B. $2n^2+2$
• C. $n^2+2$
• D. $2n^2+1$

Answer 1

The correct option is D $2n^2+1$

Given: 3, 9, 19, 33...
First term, $3=2(1{)}^2+1$
Second term, $9=2(2{)}^2+1$
Third term, $19=2(3{)}^2+1$
Fourth term, $33=2(4{)}^2+1$
Similarly, $n^{th}$ term = $2n^2+1$.
So, the algebraic expression for $n^{th}$ term of the pattern is $2n^2+1$.