Understanding Sequence Notation and Finding Next 5 Terms: Homework Help

[cdotter]

Homework Statement

[tex]a_{n+2}=3a_{n+1}-2a_n[/itex]
$$a_1=1, a_2=1$$
Find the next 5 terms.

Homework Equations

The Attempt at a Solution

I don't really understand the "a sub n" notation. Could someone do the next few terms so I can see how it's done?

 

[VeeEight]

To find a₃, for example, plug in n=1 into the first equation.

So, let n=1. Then,
a₁₊₂ = a₃ = 3a₂ - 2a₁ = 3(1) - 2(1) = 1

 

[cdotter]

$$a_{1+2}=3a_{1+1} + 2a_1$$
a_3 = 3(1)-2(1) = 1?

 

[Mark44]

Homework Statement

[tex]a_{n+2}=3a_{n+1}-2a_n[/itex]
$$a_1=1, a_2=1$$
Find the next 5 terms.

Homework Equations

The Attempt at a Solution

I don't really understand the "a sub n" notation.

The terms in the sequence are {a₁, a₂, a₃, ..., a_n, a_n+1, a_n+2, ...}.

The first formula says that to get the (n + 2)nd term in the sequence you need the preceding two terms, the (n + 1)st term and the nth term.

Could someone do the next few terms so I can see how it's done?

Well, no, but maybe you can do them. You have a₁ = 1 and a₂ = 1. Use the first formula to get a₃. Then when you have a₃, use the formula again to find a₄, and so on for as many terms as you need.

 

[cdotter]

So any possible a_n always equals 1?

 

[Mark44]

$$a_{1+2}=3a_{1+1} + 2a_1$$
a_3 = 3(1)-2(1) = 1?

The formula is

$$a_{1+2}=3a_{1+1} - 2a_1$$

 

[Mark44]

So any possible a_n always equals 1?

For this sequence, yes.

A simpler and nonrecursive definition would be a_n = 1 for n = 1, 2, 3, ...

 

[cdotter]

For this sequence, yes.

A simpler and nonrecursive definition would be a_n = 1 for n = 1, 2, 3, ...

Ok, thank you. I kept thinking I was missing something because it's stupid to ask for the next 5 terms when they're all equal to 1.