SOLUTION: The ratio of the 12th to the 10th term in a geometric series is 9:1. Find the common ratio(2 answers)
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Question 1199451: The ratio of the 12th to the 10th term in a geometric series is 9:1. Find the common ratio(2 answers)
Found 2 solutions by math_tutor2020, htmentor:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
r = common ratio
This is some nonzero value.
x = 10th term
x*r = 11th term
xr*r = xr^2 = 12th term
To get each new term, we multiply the previous term by r.
The ratio of the 12th and 10th term is (xr^2)/(x) = r^2
Therefore, r^2 = 9 leads to r = 3 or r = -3 as the two possible answers.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The n-th term of a geometric series is a_n = a*r^(n-1),
where a is the 1st term and r is the common ratio.
The 10th and 12th term are:
a_10 = a*r^9
a_12 = a*r^11
The ratio = 9 = r^11/r^9 = r^2
Thus r^2 = 9 -> r = +-3
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