A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio.
In this case, we have the first term:
- a1 = 625
and the second term:
- a2 = 125
To find the common ratio (r), we can use the formula:
r = a2 / a1
Substituting the values:
r = 125 / 625
This simplifies to:
r = 1 / 5
Now that we have the common ratio, we can find the 6th term of the sequence using the formula for the n-th term of a geometric sequence:
an = a1 * rn-1
For the 6th term (n = 6):
a6 = 625 * (1/5)6-1
Which simplifies to:
a6 = 625 * (1/5)5
Calculating (1/5)5 gives:
(1/5)5 = 1/3125
Now substituting back into the equation:
a6 = 625 * (1/3125)
This results in:
a6 = 625 / 3125 = 0.2
Therefore, the 6th term of the geometric sequence is 0.2.