SOLUTION: Which of these sequences is a geometric sequence? 1, 2, 4, 7, 11, 16, 22, … 2, 4, 8, 14, 22, 38, … 3, 6, 9, 12, 15, 18, 21, … 3, 9, 27, 81, 343, 729, …

Algebra ->  Sequences-and-series -> SOLUTION: Which of these sequences is a geometric sequence? 1, 2, 4, 7, 11, 16, 22, … 2, 4, 8, 14, 22, 38, … 3, 6, 9, 12, 15, 18, 21, … 3, 9, 27, 81, 343, 729, …      Log On


   

Question 937701: Which of these sequences is a geometric sequence?
1, 2, 4, 7, 11, 16, 22, …
2, 4, 8, 14, 22, 38, …
3, 6, 9, 12, 15, 18, 21, …
3, 9, 27, 81, 343, 729, …
Found 2 solutions by richard1234, MathLover1:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
3, 9, 27, 81, 243, 729, ..., (not 343)

Note: You may want to look up the definition of a "geometric sequence" as this question simply tests your understanding of the definition.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the sequence is geometric, then there is a common ratio, we must think in terms of multiplication previous term by common ratio r to get next term in sequence.
The r-value can be calculated by dividing any+two+consecutive terms in a geometric sequence.
The formula for calculating the Common Ratio r is:

r+=+%28nth_+term%29%2F%28%28n-1%29th+_term%29


1.
2, 4, 7, 11, 16, 22, 29, 37, …


r+=+4%2F2=2
r+=+7%2F4=1.75
r+=+11%2F7=1.571428571428571
there is no common ratio r, not a geometric sequence


2.
4, 8, 14, 22, 38, …


r+=+8%2F4=2
r+=+14%2F8=1.75
r+=+22%2F14=1.571428571428571
there is no common ratio r, not a geometric sequence

3.
6, 9, 12, 15, 18, 21, …

r+=+9%2F6=3%2F2
r+=+12%2F9=4%2F3
r+=+15%2F12=5%2F4
there is no common ratio r, not a geometric sequence

4.
9, 27, 81, 343, 729, …
r+=+27%2F9=3
r+=+81%2F27=3
r+=+343%2F81=4.24
r+=+729%2F343=2.12536443148688 there is no common ratio r, not a geometric sequence

since you have to have one solution, I think the term +343 is wrong because first three terms have common ratio 3,if we multiply 81%2A3 we got 243 and r+=243%2F81=3
and next one will be r+=+729%2F243=3
there is common ratio r=3, means the sequence 9, 27, 81, 243, 729, … IS a geometric sequence