What is the value of the fourth term in a geometric sequence for which a₁ = 30 and r = 1/2?

Solution:

A geometric sequence is a sequence made by multiplying the same value each time.

We know that

The standard geometric sequence is a, ar, ar², ar³,….

Where a represents the first term and the common ratio r is obtained by multiplying the previous term by r

n^th term is a\(_n\)= ar^{n - 1}

a = a\(_1\) = 30 and r = 1/2

To find the fourth value

a\(_4\) = 30 × (1/2)³

a\(_4\) = 30 × 1/8

a\(_n\) = 15/4

Therefore, the value of the fourth term in a geometric sequence for which a\(_1\) = 30 and r = 1/2 is 15/4.

What is the value of the fourth term in a geometric sequence for which a₁ = 30 and r = 1/2?

Summary:

The value of the fourth term in a geometric sequence for which a\(_1\) = 30 and r = 1/2 is 15/4.