Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.
–10 , 30 , –90 , ...
Write your answer using decimals and integers.
The equation to describe the sequence is the following:
T(n) = (-1)^(n+1) * 10 * 3^(n-1)
For n = 1, the equation gives:
T(1) = (-1)^(1+1) * 10 * 3^(1-1)
= (-1)^2 * 10 * 3^0
= 1 * 10 * 1
= 10
For n = 2, the equation gives:
T(2) = (-1)^(2+1) * 10 * 3^(2-1)
= (-1)^3 * 10 * 3^1
= -1 * 10 * 3
= -30
For n = 3, the equation gives:
T(3) = (-1)^(3+1) * 10 * 3^(3-1)
= (-1)^4 * 10 * 3^2
= 1 * 10 * 9
= 90
So the sequence according to the equation is:
10, -30, 90, ...