SOLUTION: The first three terms of an infinite geometric sequence are m−1, 6, m+4, where m∈ℤ Write down an expression for the common ratio, r.

Algebra ->  Sequences-and-series -> SOLUTION: The first three terms of an infinite geometric sequence are m−1, 6, m+4, where m∈ℤ Write down an expression for the common ratio, r.       Log On


   

Question 1121015: The first three terms of an infinite geometric sequence are m−1, 6, m+4, where m∈ℤ
Write down an expression for the common ratio, r.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For three consecutive terms in a geometric sequence, the square of the middle term is equal to the product of the first and last:

6%5E2+=+%28m-1%29%28m%2B4%29
m%5E2%2B3m-4+=+36
m%5E2%2B3m-40+=+0
%28m%2B8%29%28m-5%29+=+0

m = -8 or m = 5; check to see which one(s) work

m = -8: the sequence is -9, 6, -4 -- geometric with common ratio -2/3
m = 5: the sequence is 4, 6, 9 -- geometric with common ratio 3/2