# 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.

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.

## Answer: 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 9975.77.

Let's understand the solution in detail.

**Explanation:**

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 }= 9975.77.