Find the 15th term of the geometric sequence 4, -8, 16, -32, 64
To find the 15th term of a geometric sequence, we can use the formula $a_n = a_1 \cdot r^{(n-1)}$, where $a_n$ is the $n$th term, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the position of the term.
In this sequence, the first term $a_1$ is 4 and the common ratio $r$ is -2 (since each term is multiplied by -2 to get the next term).
Plugging these values into the formula, we have $a_{15} = 4 \cdot (-2)^{(15-1)} = 4 \cdot (-2)^{14}$.
Calculating this, we have $a_{15} = 4 \cdot 2^{14} = 4 \cdot 16384 = \boxed{65536}$.
To find the 15th term of a geometric sequence, we first need to determine the common ratio (r) of the sequence. We can find it by dividing any term by its preceding term. Let's take the second term (-8) divided by the first term (4):
r = -8 / 4 = -2
Now, we can use the general formula for the nth term of a geometric sequence, which is given by:
an = a1 * r^(n - 1)
where:
an = nth term
a1 = first term
r = common ratio
n = term number
We want to find the 15th term, so plugging in the values:
a15 = 4 * (-2)^(15 - 1)
Simplifying:
a15 = 4 * (-2)^14
Now, we can evaluate this expression:
a15 = 4 * 2^14
a15 = 4 * 16384
a15 = 65536
Therefore, the 15th term of the geometric sequence 4, -8, 16, -32, 64 is 65536.
To find the 15th term of the geometric sequence 4, -8, 16, -32, 64, we need to first determine the common ratio of the sequence.
The common ratio (r) can be found by dividing any term of the sequence by its previous term. Let's take the second and first terms of the sequence:
-8 / 4 = -2
The common ratio (r) is -2.
Now that we know the common ratio, we can 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, r represents the common ratio, and n represents the term number.
Plugging in the values into the formula:
A15 = 4 * (-2)^(15-1)
Simplifying the exponent:
A15 = 4 * (-2)^14
Calculating the value inside the parentheses:
A15 = 4 * 16384
A15 = 65536
Therefore, the 15th term of the given geometric sequence is 65536.