# Video: Finding the Order of a Term in a Sequence given the πth Term of That Sequence

Find π, given π_π = 4π + 5 and π_π = 237.

01:56

### Video Transcript

Find π, given ππ is equal to four π plus five and ππ is equal to 237.

What weβre actually looking at here is an expression for an arithmetic sequence. And we know that itβs an arithmetic sequence because an arithmetic sequence has a common difference. And this expression here and this sequence would have a common difference of four, as itβs the coefficient of π which is the term number. I can demonstrate this quickly by showing you. This is the first term, so π one, so our first term where weβd substitute in that π is equal to one, would be four times one plus five which gives us nine. So the first term would be nine. And our second term would be equal to four multiplied by two, cause weβve substituted π is equal to two because itβs the second term, plus five which would be equal to 13. And therefore, our second term minus our first term is equal to 13 minus nine which is equal to four which is the same as the common difference we saw as the coefficient of π.

Okay, great. So now we kind of gained understanding of what this is. We can now find what π is. Okay, so weβve got ππ is equal to four π plus five. First of all, weβre gonna substitute our value for ππ in, which gives us 237 is equal to four π plus five. So now we solve for π. The first thing we do to do that is subtract five from both sides which gives us 232 is equal to four π. Now Iβve just rewritten this with the πs on the left-hand side.

And then finally, weβre gonna divide both sides by four which gives us π is equal to 58, which means we know that the 58th term is equal to 237.