Question

What value should replace a in sigma notation to find the sum of the first 8 terms of the sequence −2,−8,−32, . . .
?(1 point)
Responses

−32
negative 32

−2
negative 2

4
4

8

Answer 1

To find the sum of the first 8 terms of the sequence \(-2, -8, -32, \ldots\), we first need to identify the pattern of the sequence.

The sequence has the following first few terms:
1. \( a_1 = -2 \)
2. \( a_2 = -8 = -2 \times 4 \)
3. \( a_3 = -32 = -2 \times 16 \)

We can see that each term is a multiple of \(-2\) multiplied by a power of 4:
- \( -2 \) can be expressed as \( -2 \times 4^0 \)
- \( -8 \) can be expressed as \( -2 \times 4^1 \)
- \( -32 \) can be expressed as \( -2 \times 4^2 \)

This suggests that the general term of the sequence can be represented as:
\[ a_n = -2 \times 4^{n-1} \]

To express the sum of the first 8 terms using sigma notation, we need to sum it from \( n = 1 \) to \( n = 8 \):
\[ S_8 = \sum_{n=1}^{8} a_n = \sum_{n=1}^{8} (-2 \times 4^{n-1}) \]

Thus, the correct value to replace \( a \) in the sigma notation (which represents the general term) is:
\[ -2 \]

So, the answer is:
**−2** (negative 2).