Write a possible explicit rule for the nth term of the sequence, then use it to find the 20th term.
5, -10, 20, -40, 80, -160....
Ans: a(n) = 5(-2)^n - 1
20th term: -2621440
one problem, you should have brackets around n-1
so a(n) = 5(-2)^(n-1)
otherwise, good job
To find the explicit rule for the nth term of the given sequence, we can observe that each term alternates between a positive and negative value. Additionally, each term is obtained by multiplying the previous term by -2. We can use this information to derive the explicit rule.
Let's break down the sequence and its corresponding indices:
Term 1: 5
Term 2: -10 (5 * (-2))
Term 3: 20 (-10 * (-2))
Term 4: -40 (20 * (-2))
Term 5: 80 (-40 * (-2))
Term 6: -160 (80 * (-2))
From this pattern, we can see that each term can be obtained by multiplying 5 by (-2) raised to the power of the previous term's index minus 1.
Therefore, the explicit rule for the nth term, denoted as a(n), can be written as:
a(n) = 5 * (-2)^(n-1)
To find the 20th term, we substitute n = 20 into the explicit rule:
a(20) = 5 * (-2)^(20-1)
= 5 * (-2)^19
= -2621440
Hence, the 20th term of the sequence is -2,621,440.