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