Question

Question
Calculate upper S subscript 35 baseline for the arithmetic sequence in which lower a subscript 5 baseline equals 19 and the common difference is lower equals negative 1.3.
(1 point)
Responses

negative 42.8
Image with alt text: negative 42.8

negative 20
Image with alt text: negative 20

73.5
73.5

124.3

Answer 1

To find the 35th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

\[
a_n = a_1 + (n - 1)d
\]

where
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.

We know from the problem statement that:
- \( a_5 = 19 \)
- The common difference \( d = -1.3 \)

First, we need to find \( a_1 \). Since \( a_5 \) is the 5th term, we can write:

\[
a_5 = a_1 + (5 - 1)(-1.3) \\
19 = a_1 + 4(-1.3) \\
19 = a_1 - 5.2 \\
a_1 = 19 + 5.2 = 24.2
\]

Now that we have \( a_1 = 24.2 \), we can find \( a_{35} \):

\[
a_{35} = a_1 + (35 - 1)(-1.3) \\
a_{35} = 24.2 + 34(-1.3) \\
a_{35} = 24.2 - 44.2 \\
a_{35} = 24.2 - 44.2 = -20
\]

So, \( S_{35} \) (which is the 35th term of the sequence) is \(-20\).

The correct response is:

**negative 20**