Question

Question 1 of 10 What is the value of the fourth term in a geometric sequence for which ay = 15 and r= 1/3? Express your answer as a fraction. Answer here​

Answer 1

The fourth term of given geometric sequence is 5/9

Explanation:

The general formula for geometric sequence is given by:

`a_n = a_1.r^((n-1))`

Here a_n is the nth term,

a_1 is the first term

and r is the common ratio.

It is given in the question that

`a_1 = 15\\r = (1)/(3)`

Putting these values

`a_n = 15 . ((1)/(3))^(n-1)`

For 4th term, we will put n=4

So,

`a_4 = 15 . ((1)/(3))^(4-1)\\a_4 = 15 . ((1)/(3))^3\\a_4 = 15 . (1)/(27)\\a_4 = (15)/(27)\\a_4 = (5)/(9)`

Hence,

The fourth term of given geometric sequence is 5/9