Write the sigma notation for the geometric series from the following finite geometric sequence: 3, 9, 27, 81, 243.(1 point)

Question

Responses

∑5n=15(3)n−1
sigma-summation underscript n equals 1 overscript 5 End Scripts 5 left parenthesis 3 right parenthesis superscript n minus 1 baseline

∑5n=13(3)n−1
sigma-summation underscript n equals 1 overscript 5 End Scripts 3 left parenthesis 3 right parenthesis superscript n minus 1 baseline

∑3n=13(3)n−1
sigma-summation underscript n equals 1 overscript 3 End Scripts 3 left parenthesis 3 right parenthesis superscript n minus 1 baseline

∑3n=15(3)n−1
sigma-summation underscript n equals 1 overscript 3 End Scripts 5 left parenthesis 3 right parenthesis superscript n minus 1 baseline

Answer 1

To represent the finite geometric series 3, 9, 27, 81, 243 in sigma notation, let's identify the terms of the series:

• The first term \( a = 3 \)
• The common ratio \( r = 3 \)

The general term of a geometric series can be represented as:

\[ a \cdot r^{n-1} \]

In this case, \( n \) starts from 1 for the first term up to the 5th term, which means \( n \) will range from 1 to 5.

Thus, the sigma notation for the series would be:

\[ \sum_{n=1}^{5} 3 \cdot 3^{n-1} \]

This matches with the option:

∑5n=13(3)n−1 (Which is equivalent to the representation above)