Help understanding this sequence.

[-Whiplash-]

So I got this sequence in my homework and I just don't understand what I'm supposed to do since it's unlike any sequence I've ever seen.

the question is as follows:

a₁=4, a₂=3, a_n=3a_n-1+2a_n-2, n>2, n∈N

Find the first 5 terms.

at first I thought a_n=3a_n-1+2a_n-2 would work so that for say a₃, is would be a₃=3a₂+2a₁ so a₃=3(3)+2(4), thus a₃=17, however I`m not sure if that's right, I know it's not a₃=3(2)+2(1), a₃=8 because when I tried that my marker in the course told me I was wrong but with no explanation as to why.

For the record, it's not sequences that are difficult for me, it's just the way this one is formatted that confuses me. thanks.

 

[pka]

the question is as follows:

a₁=4, a₂=3, a_n=3a_n-1+2a_n-2, n>2, n∈N
Find the first 5 terms.

\(\displaystyle a_3=3a_2+2a_1=3(3)+2(4)=17\)

You just have two more terms to find.

 

[-Whiplash-]

\(\displaystyle a_3=3a_2+2a_1=3(3)+2(4)=17\)You just have two more terms to find.

So I was right then? huh, okay, thanks.

 

[Deleted member 4993]

So I got this sequence in my homework and I just don't understand what I'm supposed to do since it's unlike any sequence I've ever seen.

the question is as follows:

a₁=4, a₂=3, a_n=3a_n-1+2a_n-2, n>2, n∈N

Find the first 5 terms.

at first I thought a_n=3a_n-1+2a_n-2 would work so that for say a₃, is would be a₃=3a₂+2a₁ so a₃=3(3)+2(4), thus a₃=17, however I`m not sure if that's right, I know it's not a₃=3(2)+2(1), a₃=8 because when I tried that my marker in the course told me I was wrong but with no explanation as to why.

For the record, it's not sequences that are difficult for me, it's just the way this one is formatted that confuses me. thanks.

a₁=4,

a₂=3,

a_n=3a_n-1+2a_n-2

a₃= 3a₂ + 2a₁ = 3*3 + 2*4 = 9 + 8 = 17

a₄= 3a₃ + 2a₂ = 3*17 + 2*3 = 51 + 6 = 57

and continue....