find the fourth term of the geometric sequence whose first is 200 and common ratio is 7/2
To find the fourth term of a geometric sequence, we need to use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Where:
an represents the nth term of the sequence
a1 represents the first term of the sequence
r represents the common ratio of the sequence
n represents the position of the term we want to find
In this case, we are given:
a1 = 200 (first term)
r = 7/2 (common ratio)
n = 4 (fourth term)
Using the formula, we can substitute the given values:
a4 = 200 * (7/2)^(4-1)
Simplifying the exponent:
a4 = 200 * (7/2)^3
Now, let's calculate the value inside the parentheses:
(7/2)^3 = 7^3 / 2^3 = 343 / 8
Finally, we substitute this value back into the formula:
a4 = 200 * (343/8)
To get the final answer, we multiply 200 by 343/8:
a4 = 68500/8 = 8562.5
Therefore, the fourth term of the given geometric sequence is 8562.5.