Question

Find the 12th term of the geometric sequence 5, 15, 45, ...
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Answer 1

12th term = 885735

Explanation:

Meaning: A geometric sequence is an ordered set of numbers that progresses by multiplying or dividing each term by the same number.

5 x 3 = 15

15 x 3 = 45

The number we multiply the terms by in this sequence is 3.

4th term = 45 x 3 = 135

5th term = 135 x 3 = 405

6th term = 405 x 3 = 1215

7th term = 1215 x 3 = 3645

8th term = 3645 x 3 = 10935

9th term = 10935 x 3 = 32805

10th term = 32805 x 3 = 98415

11th term = 98415 x 3 = 295245

12th term = 295245 x 3 = 885735

5, 15, 45, 135, 405, 1215, 3645, 10935, 32805, 98415, 295245, 885735

hope this helps :)

Answer 2

Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.

Explanation:

The 12th term of the geometric sequence 5, 15, 45, ... can be found using the general formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

where:

a1 is the first term of the sequence,

r is the common ratio, and

n is the position of the term that you're trying to find.

In this case,

a1 = 5

r = 15/5 = 3

n = 12

so:

a12 = 5 * 3^(12-1) = 5 * 3^11 = 5 * 177147 = 885735

Therefore, the 12th term of the geometric sequence 5, 15, 45, ... is 885735.