Write the first six terms of the sequence.$f\left(n\right)=\left(-2\right)^{n+1}$f(n)=(−2)n+1​The first six terms of the sequence are , , ,

To find the first six terms of the sequence given by the formula $f(n) = (-2)^{n+1}$, we will evaluate $f(n)$ for $n = 1, 2, 3, 4, 5,$ and $6$.

Step 1: Calculate Each Term

1. For $n = 1$: $f(1) = (-2)^{1+1} = (-2)^2 = 4$

2. For $n = 2$: $f(2) = (-2)^{2+1} = (-2)^3 = -8$

3. For $n = 3$: $f(3) = (-2)^{3+1} = (-2)^4 = 16$

4. For $n = 4$: $f(4) = (-2)^{4+1} = (-2)^5 = -32$

5. For $n = 5$: $f(5) = (-2)^{5+1} = (-2)^6 = 64$

6. For $n = 6$: $f(6) = (-2)^{6+1} = (-2)^7 = -128$

Final Answer

The first six terms of the sequence are $4, -8, 16, -32, 64, -128$.