What is the 13th term of the geometric sequence
8, −16, 32, −64,
The geometric sequence has a common ratio of -2.
To find the 13th term, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where:
an is the nth term
a1 is the first term
r is the common ratio
n is the term number
For this sequence, a1 = 8 and r = -2.
We want to find the 13th term, so n = 13.
Therefore, the formula becomes:
a13 = 8 * (-2)^(13-1)
Simplifying:
a13 = 8 * (-2)^12
a13 = 8 * 4096
a13 = 32768
The 13th term of the geometric sequence is 32768.
To find the 13th term of the geometric sequence, we first need to determine the common ratio (r).
We can observe that each term is obtained by multiplying the previous term by -2.
So, r = -2.
Now, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Given that the first term (a1) is 8, we can substitute the values into the formula to find the 13th term (a13).
a13 = 8 * (-2)^(13-1)
= 8 * (-2)^12
= 8 * 4096
= 32,768
Therefore, the 13th term of the geometric sequence 8, -16, 32, -64 is 32,768.
To find the 13th term of the geometric sequence, we need to determine the common ratio and use it to calculate the term.
In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio. In this case, the common ratio can be found by dividing any term by its preceding term.
Let's calculate the common ratio:
common ratio = (-16) / 8 = -2
Now that we know the common ratio (-2), we can find the 13th term using the formula:
term_n = initial term * (common ratio)^(n-1)
Using the formula, we can substitute the given values:
term_13 = 8 * (-2)^(13-1)
Calculating the exponent:
(-2)^(13-1) = (-2)^12 = 4096
Substituting the value back into the formula:
term_13 = 8 * 4096 = 32768
Therefore, the 13th term of the given geometric sequence 8, -16, 32, -64, ... is 32768.