Answer:
The first six terms of the sequence [tex]f\left(n\right)=\left(-3\right)^n[/tex] are:
[tex]-3, 9, -27, 81, -243, 729[/tex]
Step-by-step explanation:
Given the sequence
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
Here [tex]n[/tex] represents any term number in the sequence
Determining the first term
substitute n = 1 in the sequence to determine the first term
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
[tex]\:f\left(1\right)=\left(-3\right)^1[/tex]
[tex]f\left(1\right)=-3[/tex]
Thus, the first term is -3.
Determining the 2nd term
substitute n = 2 in the sequence to determine the 2nd term
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
[tex]\:f\left(2\right)=\left(-3\right)^2[/tex]
[tex]\:f\left(2\right)=9[/tex]
Thus, the 2nd term is 9.
Determining the 3rd term
substitute n = 3 in the sequence to determine the 3rd term
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
[tex]f\left(3\right)=\left(-3\right)^3[/tex]
[tex]f\left(3\right)=-27[/tex]
Thus, the 3rd term is -27.
Determining the 4th term
substitute n = 4 in the sequence to determine the 4th term
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
[tex]f\left(4\right)=\left(-3\right)^4[/tex]
[tex]f\left(4\right)=81[/tex]
Thus, the 4th term is 81.
Determining the 5th term
substitute n = 5 in the sequence to determine the 5th term
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
[tex]f\left(5\right)=\left(-3\right)^5[/tex]
[tex]f\left(5\right)=-243[/tex]
Thus, the 5th term is -243.
Determining the 6th term
substitute n = 6 in the sequence to determine the 6th term
[tex]f\left(n\right)=\left(-3\right)^n[/tex]
[tex]f\left(6\right)=\left(-3\right)^6[/tex]
[tex]f\left(6\right)=729[/tex]
Thus, the 6th term is 729
Therefore, the first six terms of the sequence [tex]f\left(n\right)=\left(-3\right)^n[/tex] are:
[tex]-3, 9, -27, 81, -243, 729[/tex]
