Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

3,18/5, 108/25...
Find the 10th term

Answer 1

15.479

Explanation:

This is a geometric series with common ratio of 6/5
Any term is 6/5 times the previous term

The general formula for the nth term of a geometric series given the common ration r and the first term a₁ is

`a_n = a_1\cdot r^(n-1)`

Here r = 6/5 and n = 10

So the 10th term is

`a_(10) = 3\cdot((6)/(5))^9`

= 3 x (6⁹/5⁹) = 3 x (10077696/1953125) = 30233088/1953125 = 15.479