Question

Given the following finite geometric sequence, write the sigma notation for the geometric series by dragging the values into the correct boxes.
8, 40, 200, 1000, 5000


5^ ∑ _ * _^n-1

A. 4
B. 5
C. 8
D. 1/5

Answer 1

To express the given finite geometric sequence \( 8, 40, 200, 1000, 5000 \) in sigma notation, we first identify the first term and the common ratio of the sequence.

Identifying the first term (\( a \)) and the common ratio (\( r \)):
- The first term \( a = 8 \).
- The second term is \( 40 \), so the common ratio \( r \) can be calculated as:
\[
r = \frac{40}{8} = 5
\]

The series can be written in sigma notation as follows:
\[
\sum_{n=1}^{5} 8 \cdot 5^{n-1}
\]

This aligns with the format given: \( 5^ \sum _ * _^{n-1} \).

In this case:
- The first box (base of the exponent \( 5 \)): **B. 5**
- The second box (the coefficient in front of the series): **C. 8**
- The last box, which is always \( n-1 \), does not need a value dragged in; it's part of the sigma notation.

Putting this together, the completed sigma notation for the series is:
\[
8 \cdot 5^{n-1}
\]
with the other identified parts as necessary (the values to drag in):

B. 5 (the base of the exponent),

C. 8 (the coefficient).