Question 1133165


{{{8}}},{{{18}}},{{{30}}},{{{44}}} -> find differences first

{{{8}}}.........{{{18}}}..........{{{30}}}..........{{{44}}}
.....{{{10}}}.........{{{12}}}...........{{{14}}}


The pattern goes +{{{10}}}, +{{{12}}}, +{{{14}}}, ...

Since the second difference is always +{{{2}}}, the nth term must involve {{{n^2}}}.

So let's say the nth number in the sequence = {{{n^2 + an + b}}}

To find {{{b}}}, you can substitute in {{{n=0}}}, i.e. what is the "zeroth" number in the sequence? In other words, what number would have come before {{{8}}}?

This number must have been {{{0}}}, in order to continue the pattern of +{{{8}}}, +{{{10}}}, +{{{12}}}, +{{{14}}}, ...

So we now know the nth number = {{{n^2 + an}}}

Now just plug in any other value we know, to find the value of{{{ a}}}. For example, using the first number in the sequence ({{{n=1}}}), we get:
{{{1 + a = 8}}}
{{{a = 7}}}


Therefore the nth term in this sequence is: {{{n^2 + 7n }}}