Question

Which equation should be used to calculate upper S subscript 9 baseline for the arithmetic sequence a subscript n baseline equals 3 n minus 1?
(1 point)
Responses

upper S subscript 9 baseline equals Start Fraction 9 over 2 End Fraction left-parenthesis 2 plus 26 right-parenthesis
Image with alt text: upper S subscript 9 baseline equals Start Fraction 9 over 2 End Fraction left-parenthesis 2 plus 26 right-parenthesis

upper S subscript 9 baseline equals Start Fraction 9 over 2 End Fraction left-parenthesis 4 plus 17 right-parenthesis
Image with alt text: upper S subscript 9 baseline equals Start Fraction 9 over 2 End Fraction left-parenthesis 4 plus 17 right-parenthesis

upper S subscript 9 baseline equals Start Fraction 9 over 4 End Fraction left-parenthesis 2 plus 26 right-parenthesis
Image with alt text: upper S subscript 9 baseline equals Start Fraction 9 over 4 End Fraction left-parenthesis 2 plus 26 right-parenthesis

upper S subscript 9 baseline equals Start Fraction 9 over 4 End Fraction left-parenthesis 4 plus 26 right-parenthesis

Answer 1

To find the sum of the first 9 terms of the arithmetic sequence \( a_n = 3n - 1 \), we first need to identify the first term \( a_1 \) and the ninth term \( a_9 \).

1. **Calculate the first term \( a_1 \)**:
\[
a_1 = 3(1) - 1 = 2
\]

2. **Calculate the ninth term \( a_9 \)**:
\[
a_9 = 3(9) - 1 = 27 - 1 = 26
\]

3. **Use the formula for the sum of the first \( n \) terms of an arithmetic sequence**:
The formula for the sum of the first \( n \) terms \( S_n \) of an arithmetic sequence is:
\[
S_n = \frac{n}{2} \times (a_1 + a_n)
\]
where \( a_n \) is the nth term.

4. **Now substitute \( n = 9 \), \( a_1 = 2 \), and \( a_9 = 26 \)**:
\[
S_9 = \frac{9}{2} \times (2 + 26) = \frac{9}{2} \times 28
\]

Thus, the equation that represents the sum of the first 9 terms is:
\[
S_9 = \frac{9}{2} \times (2 + 26)
\]

Therefore, the correct response is:
\[
\text{upper } S_9 = \frac{9}{2} \left(2 + 26\right)
\]