# Which sequence shows a pattern where each term is 1.5 times the previous term and the first term is 3? Find its 21st term.

**Solution:**

Arithmetics Progressions are sequences in which the consecutive terms are related by a common difference. Geometric sequences are sequences in which the consecutive terms are related by a common ratio. Let's understand the solution in detail.

The sequence where each term is 1.5 times the previous term is a geometric progression with a common ratio r = 1.5.

Now, the first term a is given to be 3, i.e, a = 3.

Hence, we can find the geometric sequence, the general form of which is given by a, ar, ar^{2}, ar^{3},......,ar^{n - 1}.

Hence, using the above formula, we get the sequence as 3, 4.5, 6.75, 10.125,...

The nth term of the series is given by ar^{n - 1}.

Therefore, using the above formula, we get the 21st term as 3(1.5)^{20 }= 9975.75

Hence, the sequence that shows a pattern where each term is 1.5 times the previous term and the first term is 3, is 3, 4.5, 6.75, 10.125, and so on. Its 21st term is 9975.75

## Which sequence shows a pattern where each term is 1.5 times the previous term and the first term is 3? Find its 21st term.

**Summary:**

The sequence that shows a pattern where each term is 1.5 times the previous term and the first term is 3 is; 3, 4.5, 6.75, 10.125 and so on. Its 21st term is 9975.75

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