Question

Find the missing number by observing the number pattern.
1, 7, 17,___, 49, 71

• A. 33
• B. 24
• C. 37
• D. 31

Answer 1

The correct option is D 31

We've to find the missing number in the pattern.
So, first we've to find an algebraic expression by which we are getting these terms.
We can write terms of the given pattern as,
$1=2\times (1{)}^2-1[1^{st}]$
$7=2\times (2{)}^2-1[2^{nd}]$
$17=2\times (3{)}^2-1[3^{rd}]$

Similarly for the $n^{th}$ term, we can write $2\times n^2-1$.

Here, we've to find the $4^{th}$ term.
Using $n=4$ in $2\times n^2-1$, we have
$\Rightarrow 2\times 4^2-1=2\times 16-1=32-1=31$

$\Rightarrow$ 31 will be the missing number in the given number pattern.
Hence, option d is correct.