Question

Write the sigma notation for the geometric series from the following finite geometric sequence: 100, 80, 64.(1 point)
Responses

∑100n=13(0.8)^n−1
the sum from n is equal to 1 to 100 of 3

∑3n=1100(0.8)^n−1
the sum from n is equal to 1 to 3 of 100

∑3n=11.2(100)^n−1
the sum from n is equal to 1 to 3 of 1 point 2

∑3n=1100(3)^n−1

Answer 1

To express the given finite geometric sequence 100, 80, 64 in sigma notation, we first need to identify the first term, the common ratio, and the number of terms.

1. **First term (a)**: The first term is 100.
2. **Common ratio (r)**: The common ratio can be calculated as follows:
\[
r = \frac{80}{100} = 0.8 \quad \text{and} \quad \frac{64}{80} = 0.8
\]
Therefore, the common ratio is 0.8.
3. **Number of terms (n)**: There are 3 terms in this sequence.

Now, we can set up the sigma notation:
\[
\sum_{n=1}^{3} 100(0.8)^{n-1}
\]

This notation captures the series as it starts from \(n=1\) to \(n=3\), with the first term being 100 and each subsequent term being multiplied by the common ratio \(0.8\).

Thus, the correct choice from the provided options is:

**∑3n=1100(0.8)^{n−1}** (the sum from \(n=1\) to \(3\) of \(100\)).