Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


–10 , 30 , –90 , ...


Write your answer using decimals and integers.

Answer 1

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, ...