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.