Enter the next three terms in the geometric sequence. Round to the nearest tenth value.

36, 54, 81, 121.5, ...

The next three terms of the sequence are 182.3, 273.5 and 410.3 respectively (all rounded to the nearest tenth value)

Step-by-step explanation:

A geometric sequence is one in which successive members are multiples of a constant common ratio.

From the sequence, we can identify that;

First term a = 36

common difference = 2nd term/first term = 3rd term/second term = 4th term/3rd term

Hence, common difference d = 54/36 = 81/54 = 1.5

The next three terms of the sequence are the 5th, 6th and 7th term respectively.

For the 5th term, we have 4th term * common ratio = 121.5 * 1.5 = 182.3

For the 6th term, we have 5th term * common ratio = 182.3 * 1.5 = 273.5

For the 7th term, we have 6th term * common ratio = 273.5 * 1.5 = 410.3