Question

Sequence help (I hate these)

Answer 1

Let me type

Answer 2

What is the sequence?

Answer 3

\[S_{n}= 2(S_{n-1)}-4\]

Answer 4

I know this reads as "double the previous term and subtract 4"
They give S1 as 6.

Answer 5

So the previous term is 5, right?

Answer 6

They give S1, which is 6, and want S5

Answer 7

So I do not know if the previous term is supposed to be 5, or what they give, 6.

Answer 8

Sorry I don't recognize the problem

Answer 9

Any ideas?? I hope it is really not this hard.

Answer 10

This is a recurrence relation where one term depends on the previous, but the buck stops at n=0, which is usually a constant, say k, or the starting term.

An easy way (but involves a little more work) to solve this is to expand the sequence and try to find the pattern.
Say we have a sequence with a starting term S0=k, and the recurrence relation is
S(n)=aS(n-1)-b
Then
S(0)=k
S(1)=ak-b
S(2)=a(ak-b)-b=a^2k-ab-b
S(3)=a(a(ak-b)-b)-b=a^3k-a^2b-ab-b=a^3k-b(a^2+a+1)
S(4)=a(a(a(ak-b)-b)-b)-b=a^4k--a^3b-a^2b-ab-b=a^4k-b(a^3+a^2+a+1)
So for the nth term,
S(n)=a^n(k)-b(a^(n-1)+a^(n-2)+....+a+1)
=a^n(k)-b(a^n-1)/(a-1) ........ using the identity (a^n-1)/(a-1)=a^(n-1)+....a^2+a+1

So can you take it from here?

Note: there are more advanced ways of solving this problem involving a little more theory, but simpler calculations. These are typically computer science subject matter (discrete math or combinatorics). If you're working on these courses, we will take a different approach.

Answer 11

Well, I was told in a PM to start with 6 cause it is s1. Here is what I did.