Answer:
205.03125
Explanation:
You want the 8th term of the sequence that begins 12, 18, 27, ....
Differences
The first differences of the given terms are ...
18 -12 = 6
27 -18 = 9
These are not constant, so the sequence is not an arithmetic sequence.
Ratios
The ratios of sequential terms are ...
18/12 = 1.5
27/8 = 1.5
These are constant, suggesting the sequence is an exponential sequence. The equation for the n-th term is ...
an = 12(1.5^(n-1))
Then the 8th term is ...
a8 = 12(1.5^7) = 205.03125
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Additional comment
The sequence could be quadratic if the second differences are all 9-6=3. In that case, the equation for the n-th term is ...
an = 1.5n(n +1) +9
and the 8th term is ...
a8 = 1.5·8(8+1) +9 = 117
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