write an equation to decribe the sequence below. use n to represent the position of a term in the sequence, where n=1 for the first term
-24,-48,-96
write your answer using decimals and integers
The equation to describe the sequence is:
a(n) = -24 * 2^(n-1)
where:
- a(n) represents the nth term in the sequence,
- n represents the position of the term in the sequence starting from 1, and
- 2^(n-1) represents the exponential function where the base is 2 and the exponent is (n-1).
Using this equation, when n=1, the first term is given by:
a(1) = -24 * 2^(1-1)
= -24 * 2^0
= -24 * 1
= -24
Similarly, when n=2, the second term can be found:
a(2) = -24 * 2^(2-1)
= -24 * 2^1
= -24 * 2
= -48
And when n=3, the third term is:
a(3) = -24 * 2^(3-1)
= -24 * 2^2
= -24 * 4
= -96
Thus, the equation a(n) = -24 * 2^(n-1) represents the given sequence -24, -48, -96.