what is the 12th term of the geometric sequence: 40, 84, 176.4, 370.44…
To find the 12th term of the geometric sequence, we first need to determine the common ratio (r).
We can calculate the common ratio by dividing any term by its preceding term.
For example, the second term (84) divided by the first term (40) gives us a common ratio, r, of 2.1. Similarly, dividing the third term (176.4) by the second term (84) also gives us a common ratio of 2.1. This confirms that the common ratio (r) is indeed 2.1.
Now that we know the common ratio is 2.1, we can use the formula for the nth term of a geometric sequence:
tn = ar^(n-1)
where:
tn is the nth term
a is the first term
r is the common ratio
n is the number of terms
We know the first term, a, is 40, the common ratio, r, is 2.1, and we need to find the 12th term, so n = 12.
t12 = 40 * (2.1)^(12-1)
t12 = 40 * (2.1)^11
t12 ≈ 40 * 250.048
Calculating this, we find that the 12th term of the geometric sequence is approximately 10,001.92.
To find the 12th term of the geometric sequence, we need to first determine the common ratio.
To do this, we'll divide any term by the previous term in the sequence.
Let's divide the second term (84) by the first term (40):
84/40 = 2.1
Let's divide the third term (176.4) by the second term (84):
176.4/84 = 2.1
We observe that the common ratio is 2.1.
Now that we know the common ratio, we can find the 12th term using the formula:
Tn = a * r^(n-1)
Where:
Tn = the nth term
a = the first term
r = the common ratio
n = the term number we want to find
Plugging in the values:
a = 40 (the first term)
r = 2.1 (the common ratio)
n = 12 (the term number we want to find)
T12 = 40 * 2.1^(12-1)
Simplifying:
T12 = 40 * 2.1^11
Calculating:
T12 ≈ 8765.460
Therefore, the 12th term of the geometric sequence is approximately 8765.460.