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

excefebraxp
2022-09-13
Answered

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

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Willie Smith

Answered 2022-09-14
Author has **18** answers

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 squablack, shown by ${(n+1)}^{2}=x$

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

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

$x=49$

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 squablack, shown by ${(n+1)}^{2}=x$

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

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

$x=49$

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