# math...

posted by on .

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, ar2,, ar3,, ar4,, ...

I don't think you have the first one correct. It should be
tn = 5tn-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.

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.