# What is the next number in the sequence ___, ___, 16, 25, 36?

Aug 6, 2018

The next number is $49$

#### Explanation:

If we consider the first blank as the first term, then
16 is the third term
25 is the fourth term
36 is the fifth term

We can see that all the numbers shown are perfect squares. We know ${4}^{2} = 16$, ${5}^{2} = 25$, and ${6}^{2} = 36$

So we can find a rule, using $n$ for term
Since ${4}^{2} = 16$ is the third term, we can see that the term plus one is what is being squared, shown by ${\left(n + 1\right)}^{2} = x$

Now to find the 6th term we can use this rule and solve for $x$

${\left(6 + 1\right)}^{2} = x$

$x = 49$