Question
Find the 15th term of the geometric sequence 4, -8, 16, -32, 64
Answers
GPT 3.5
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 $a_{15} = 4 \cdot 2^{14} = 4 \cdot 16384 = \boxed{65536}$.
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 $a_{15} = 4 \cdot 2^{14} = 4 \cdot 16384 = \boxed{65536}$.