Whats the difference between recursive formula and general term?

[supernova1203]

To solve this question i came up with what i think is the recursive formula, the question is in the attachment, the recursive formula i came up with is

Tn=tn-1+2 when t1=8

using the formula i can solve the questions but then it asks me to come up with a general term as well...what is the difference between the recursive formula and the general term? Are they the same thing as i think they are?

 

[eumyang]

When you're asked to find the general term, you are asked for an expression that usually involves variables. This general term can be defined recursively or non-recursively. For instance, if you have a sequence defined as follows:
1, 4, 7, 10, ...

1 is the 1st term (or t₁).
4 is the 2nd term (or t₂).
7 is the 3rd term (or t₃).
10 is the 4th term (or t₄).

I want to find the nth term of the sequence, or t_n. I note that each successive term is 3 more than the previous, so I could define it recursively as thus:
t_n = t_n-1 + 3, with t₁ = 1

Or I could define it non-recursively, which I think is the better way to go:
t_n = 3n + 1

I like the 2nd way better in this case (and in your problem), because you're not required to find the previous terms. Say you want to find the 100th term. It will be quicker to use the non-recursive formula.

 

[supernova1203]

When you're asked to find the general term, you are asked for an expression that usually involves variables. This general term can be defined recursively or non-recursively. For instance, if you have a sequence defined as follows:
1, 4, 7, 10, ...

1 is the 1st term (or t₁).
4 is the 2nd term (or t₂).
7 is the 3rd term (or t₃).
10 is the 4th term (or t₄).

I want to find the nth term of the sequence, or t_n. I note that each successive term is 3 more than the previous, so I could define it recursively as thus:
t_n = t_n-1 + 3, with t₁ = 1

Or I could define it non-recursively, which I think is the better way to go:
t_n = 3n + 1

I like the 2nd way better in this case (and in your problem), because you're not required to find the previous terms. Say you want to find the 100th term. It will be quicker to use the non-recursive formula.

ah... ty :)