the first term of a sequence of numbers is 1. if each term after the first is the product of -2 and the preceding term, what is the 6th term of the sequence?
How do I approach this problem?
(-2)^5
To approach this problem, let's break it down step by step:
Step 1: Identify the pattern
We are given that the first term is 1, and each term after the first is the product of -2 and the preceding term. This means that each term is obtained by multiplying the previous term by -2.
Step 2: Calculate the subsequent terms
Starting with the first term, we can calculate the subsequent terms using the given pattern:
Second term = -2 * first term = -2 * 1 = -2
Third term = -2 * second term = -2 * (-2) = 4
Fourth term = -2 * third term = -2 * 4 = -8
Fifth term = -2 * fourth term = -2 * (-8) = 16
Step 3: Determine the sixth term
Following the pattern, we can calculate the sixth term by multiplying the fifth term by -2:
Sixth term = -2 * fifth term = -2 * 16 = -32
Therefore, the sixth term of the sequence is -32.