Question

What is the first six terms of the sequence f(n)=(-3)^n​

Answer 1

The first six terms of the sequence
`f\left(n\right)=\left(-3\right)^n` are:

`-3, 9, -27, 81, -243, 729`

Explanation:

Given the sequence

`f\left(n\right)=\left(-3\right)^n`

Here
`n` represents any term number in the sequence

Determining the first term

substitute n = 1 in the sequence to determine the first term

`f\left(n\right)=\left(-3\right)^n`

`\:f\left(1\right)=\left(-3\right)^1`

`f\left(1\right)=-3`

Thus, the first term is -3.

Determining the 2nd term

substitute n = 2 in the sequence to determine the 2nd term

`f\left(n\right)=\left(-3\right)^n`

`\:f\left(2\right)=\left(-3\right)^2`

`\:f\left(2\right)=9`

Thus, the 2nd term is 9.

Determining the 3rd term

substitute n = 3 in the sequence to determine the 3rd term

`f\left(n\right)=\left(-3\right)^n`

`f\left(3\right)=\left(-3\right)^3`

`f\left(3\right)=-27`

Thus, the 3rd term is -27.

Determining the 4th term

substitute n = 4 in the sequence to determine the 4th term

`f\left(n\right)=\left(-3\right)^n`

`f\left(4\right)=\left(-3\right)^4`

`f\left(4\right)=81`

Thus, the 4th term is 81.

Determining the 5th term

substitute n = 5 in the sequence to determine the 5th term

`f\left(n\right)=\left(-3\right)^n`

`f\left(5\right)=\left(-3\right)^5`

`f\left(5\right)=-243`

Thus, the 5th term is -243.

Determining the 6th term

substitute n = 6 in the sequence to determine the 6th term

`f\left(n\right)=\left(-3\right)^n`

`f\left(6\right)=\left(-3\right)^6`

`f\left(6\right)=729`

Thus, the 6th term is 729

Therefore, the first six terms of the sequence
`f\left(n\right)=\left(-3\right)^n` are:

`-3, 9, -27, 81, -243, 729`