Question

The nth term of a sequence is given by (-1)^n-2 2^n-1. Find the sum of the second and third terms

Answer 1

To find the sum of the second and third terms of the sequence given by the nth term \( a_n = (-1)^{n-2} 2^{n-1} \), we first calculate the specific terms:

1. **Calculate the second term (\( a_2 \))**:
\[
a_2 = (-1)^{2-2} 2^{2-1} = (-1)^0 2^1 = 1 \cdot 2 = 2
\]

2. **Calculate the third term (\( a_3 \))**:
\[
a_3 = (-1)^{3-2} 2^{3-1} = (-1)^1 2^2 = -1 \cdot 4 = -4
\]

3. **Sum the second and third terms**:
\[
a_2 + a_3 = 2 + (-4) = 2 - 4 = -2
\]

Thus, the sum of the second and third terms is \(\boxed{-2}\).