SOLUTION: Hi, My sister has an exam tomorrow and I am helping her study.We are having a problem with sequence equations. It gives a sequence like 2,5,8,11 and wants us to find the 23rd term.

Question 256103: Hi, My sister has an exam tomorrow and I am helping her study.We are having a problem with sequence equations. It gives a sequence like 2,5,8,11 and wants us to find the 23rd term. now I understand the first part which is to figure out the the number between the two terms and times it with the term you want to find, but then for some reason her book says to add a number to get the answer and I am so confused. the most I can get is t=3n and then I am stuck please help us.
thank you
Kaitlynn
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Lets assume the sequence 2,5,8,11,... is an arithmetic sequence. The general form of the arithmetic sequence is

where is the nth term, d is the difference, and is the first term

So lets find the difference between 2 terms (i.e. the difference between two terms)
====================================================================================================================

To find the difference, simply pick any term and subtract the previous term from that selected term

Select the 2nd term (which is 5) and subtract the 1st term (which is 2) from it.

So we get a difference of

Lets pick another pair of terms to verify:

Select the 3rd term (which is 8) and subtract the 2nd term (which is 5) from it.

And again, we get a difference of
-----------------------------------------------------

Lets pick another pair of terms to verify:

Select the 4th term (which is 11) and subtract the 3rd term (which is 8) from it.

And again, we get a difference of

====================================================================================================================
Since we've tested every consecutive pair of terms, we've verified that the sequence has a constant difference of . This means the sequence is arithmetic

Since the difference is and the first term is , this means the arithmetic sequence is

where starts at

So the list of numbers 2,5,8,11... can be generated by the sequence

where starts at

Since n=0 generates the first term, this means that the 23rd term is generated when n=22

Start with the given formula.

Plug in

Multiply

Add

So the 23rd term is 68
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