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)
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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
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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
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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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