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Sequences Help!!!

This is a two part question, can somebody please me work it out:
3. A sequence a1,a2,a3,....... is defined by
a1=3
an+1= 3an-5, n>1

A. Find the value of a2 and the value of a3
B. Calculate the value of
5

ar
r=1

Can somebody please help as the wording has completely thrown me.

Reply 1

James

It means that the first term in the sequence is

a_1=3

, and each term after that is given by the formula

a_{n+1}=3a_n-5

. So to get the next term, you multiply the previous term by 3, and then subtract 5.

a_2

just means the second term, and so on.

\displaystyle\sum_{r=1}^{5}a_r

means the sum of the first five terms.

Reply 2

AveUgotaWkdSide

But that would give me this:
a2= 3(3)-5=4
a3= 3(4)-5=7

That looks right but of you do a4:
a4= 3(7)-5=16

It all goes wrong there isn't a sequence anymore

Reply 3

James

AveUgotaWkdSide

a3= 3(4)-5=8

Well that's not right, is it?

What you get will be a sequence, even though the numbers won't go up by a fixed amount each time. Don't worry about that.