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12, 18,27,...
Find the 8th term.

2 Answers

4 votes

Check the picture below.

12, 18,27,... Find the 8th term.-example-1
User Xenobiologist
by
3.2k points
4 votes

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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User Krial
by
3.7k points