Question

how can I tell if a sequences is airthmetic, geometric or neither?

determine the first three terms of each and determine if each are airthmetic, geometric or neither.

1) tn=5t n-1+ 3 wheret 1=2
first three terms: 3,13,23
airthmetic

2)t(n)= -3(4)^n
first three terms:-12,-48,-192
neither

3) tn= 2+ 5n
first three terms: 7,12,17
geometric

thnks for taking the time in checking my work I really appreciate it!


The third is an arithmetic...notice it increases by five each term. The others are correct.


An arithmetic sequence increases by a fixed amount each term, e.g.,
2, 6, 10, 14, ... 2 + 4(n-1)

A geometric sequence increases by a common ratio
a, ar, ar^2,, ar^3,, ar^4,, ...

I don't think you have the first one correct. It should be
t_n = 5t_n-1 + 3 with t₁ = 2
I think you're confusing the index for a variable. The index tells us what position the term is in the sequence.
The first few terms are 2,13,68,343
This is not an arithmetic sequence.

Your second one looks correct.

The third is not geometric.

BTW, I may've answered one of your previous questions incorrectly, I need to recheck the difference between geometric and exponential. I may have to look at the question again too.