SOLUTION: Can someone Please help me solve this problem, Thank You very much!!! Determine whether f is a geometric sequence. Identify the common ratio when possible n, 1, 2, 3,

Algebra ->  Rational-functions -> SOLUTION: Can someone Please help me solve this problem, Thank You very much!!! Determine whether f is a geometric sequence. Identify the common ratio when possible n, 1, 2, 3,       Log On


   

Question 764814: Can someone Please help me solve this problem, Thank You very much!!!
Determine whether f is a geometric sequence. Identify the common ratio when possible
n, 1, 2, 3, 4
f(n) 4, 20, 100 ,500
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f is not a geometric sequence.
B. f is a geometric sequence with r = ___
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If there is such a common ratio r, then this is a geometric sequence.
If this is a geometric series, construct the formula:

f%28n%29+=+f%281%29+%2A+r%5E%28n-1%29
use the formula to find r in our example:
n| 1, 2, 3, 4
f%28n%29| 4, 20, 100 ,500+
f%281%29+=+4.....plug in f%28n%29+=+f%281%29+%2A+r%5E%28n-1%29
f%28n%29+=+4%2A+r%5E%28n-1%29
f%282%29+=+20
f%282%29+=+4%2A+r%5E%282-1%29=20
=> 4%2A+r%5E%282-1%29=20...solve for r
r%5E1=20%2F4
r=5
then sequence formula is: f%28n%29+=+4%2A+5%5E%28n-1%29
check it:
f%28n%29+=+4%2A+5%5E%28n-1%29
n| 1, 2, 3, 4
f%28n%29| 4, 20, 100 ,500+
f%281%29+=+4%2A+5%5E%281-1%29
f%281%29+=+4%2A+5%5E0
f%281%29+=+4%2A+1
f%281%29+=+4..............true
f%282%29+=+4%2A+5%5E%282-1%29
f%282%29+=+4%2A+5%5E1
f%282%29+=+4%2A+5
f%282%29+=+20..............true
f%283%29+=+4%2A+5%5E%283-1%29
f%283%29+=+4%2A+5%5E2
f%283%29+=+4%2A+25
f%283%29+=+100..............true
f%284%29+=+4%2A+5%5E%284-1%29
f%284%29+=+4%2A+5%5E3
f%284%29+=+4%2A+125
f%284%29+=+500..............true
since all true, your answer is: B. f is a geometric sequence with r+=5