what is the 7th term of the geometric sequence 10,2.2/5,2/25 (solve here)
The progression divides by 5.
To find the 7th term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where:
an is the nth term of the sequence,
a1 is the first term of the sequence,
r is the common ratio, and
n is the term number we want to find.
In this case, the first term (a1) is 10, and the common ratio (r) can be found by dividing any term by its preceding term. So, let's calculate the common ratio:
r = (2.2/5) / 10
r = 0.22 / 5
r = 0.044
Now we can plug the values into the formula to find the 7th term (a7):
a7 = 10 * (0.044)^(7-1)
a7 = 10 * (0.044)^6
Now, we can calculate it step by step:
a7 = 10 * 0.044 * 0.044 * 0.044 * 0.044 * 0.044 * 0.044
a7 ≈ 0.0002
So, the 7th term of the geometric sequence 10, 2.2/5, 2/25 is approximately 0.0002.