please help me with sequences, in a arithmetic "word" problem

[elajhaw]

I normally know how to find the rest of a sequence,or the common difference, with multiple numbers. Being just given the equation I'm a confused, can someone please help!

 

[MarkFL]

Unless you are familiar with methods for solving linear difference equations to get a closed form, your best bet here is to manually/recursively compute the fifth term. For example, the second term is:

\(\displaystyle a_2=3a_1+2=3(1)+2=5\)

So, what would \(\displaystyle a_3\) be?

 

[ksdhart2]

Another way of approaching the problem is to try and transform the given equation into a more familiar form. In this case, that might be to translate it into words. The recursive definition tells you "each term (a_n) is three times the previous term (a_n-1) plus two." Behind the scenes, this is exactly the same approach as MarkFL outlined, but this way might feel easier to you due to being more comfortable with it.