SOLUTION: 2, 6 , 18 , 54 , .... In the sequence above what would be the 8th term?

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Question 117752: 2, 6 , 18 , 54 , ....
In the sequence above what would be the 8th term?
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The terms are
2 = 2
2x3 = 6
2x3x3 = 18
2x3x3x3 = 54
.
.
2%2A3%5En where n = 0,1,2,3...
The 8th term would be
2%2A3%5E7+=+4374 by my calculator

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

First find the pattern:

The difference between 2 and 6 is 4
The difference between 6 and 18 is 12=+3%2A4
The difference between 18 and 54 is 36+=+9%2A4=3%5E2%2A4

So,

Ratio: 3
Term 0: 2
General Term: 2%283%5Ex%29 where x is element of (0,1,2,3,4,5,……)


the 8th term of the will be: 2%283%5E8%29+=+2%2A6561=13122

check:
General Term: 2%283%5Ex%29
x=0
Term 0: 2%283%5E0%29+=+2%2A1=2

x=1
Term 1: 2%283%5E1%29+=+2%2A3=6
x=2
Term 2: 2%283%5E2%29+=+2%2A9+=+18
x=3
Term 3: 2%283%5E3%29+=+2%2A27=54
x=4
Term 4: 2%283%5E4%29+=+2%2A81=162
x=5
Term 5: 2%283%5E5%29+=+2%2A243=486

x=6
Term 6: 2%283%5E6%29+=+2%2A729=+1458
x=7
Term 7: 2%283%5E7%29+=+2%2A2187=+4374
x=8
Term 8: 2%283%5E8%29+=+2%2A6561=+13122