Find the fourth term (a4) of geometric sequence if the first term (a1) is 2 and the common ratio, r is 4.

81 54

term 4 = a r^3

= 2(4^3) = 2(64) = 128

In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio, denoted as 'r'.

Given:
First term (a1) = 2
Common ratio (r) = 4

To find the fourth term (a4), we can use the following formula:
an = a1 * rn-1

Substituting the given values:
a4 = a1 * r4-1

Simplifying the formula:
a4 = a1 * r3

Now, let's plug in the values:
a4 = 2 * 4^3

Calculating:
a4 = 2 * 64

Simplifying further:
a4 = 128

Therefore, the fourth term (a4) of the geometric sequence with a first term (a1) of 2 and a common ratio (r) of 4 is 128.

To find the fourth term (a4) of a geometric sequence, we can use the formula:

an = a1 * r^(n-1)

Where:
an = nth term
a1 = first term
r = common ratio
n = term number

In this case:
a1 = 2 (first term)
r = 4 (common ratio)
n = 4 (term number)

Substituting these values into the formula:

a4 = a1 * r^(4-1)
= 2 * 4^(4-1)
= 2 * 4^3
= 2 * 64
= 128

Therefore, the fourth term (a4) of the geometric sequence is 128.