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.
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.
To determine if a sequence is arithmetic, geometric, or neither, there are a few steps you can follow:
1. Calculate the differences between consecutive terms:
- For an arithmetic sequence, the differences between consecutive terms should be constant.
- For a geometric sequence, the ratios between consecutive terms should be constant.
2. Examine the differences or ratios to determine if they are constant:
- If the differences between consecutive terms are the same, the sequence is arithmetic.
- If the ratios between consecutive terms are the same, the sequence is geometric.
Now, let's apply these steps to the sequences you provided.
1) tn = 5t n-1 + 3 where t1 = 2
First three terms: 3, 13, 23
To find the differences, we subtract each term from its previous term:
13 - 3 = 10
23 - 13 = 10
Since the differences are constant, this sequence is arithmetic.
2) t(n) = -3(4)^n
First three terms: -12, -48, -192
To find the ratios, we divide each term by its previous term:
-48 / -12 = 4
-192 / -48 = 4
Since the ratios are constant, this sequence is geometric.
3) tn = 2 + 5n
First three terms: 7, 12, 17
To find the differences, we subtract each term from its previous term:
12 - 7 = 5
17 - 12 = 5
Since the differences are constant, this sequence is also arithmetic.
Therefore, based on the calculations, the first sequence is arithmetic, the second sequence is geometric, and the third sequence is arithmetic.
Remember to always check your calculations and verify the pattern to determine the type of sequence accurately.