Question

11-5 65th term

Answer 1

To find the 65th term of the arithmetic sequence that starts at 11 and has a common difference of -5, we can use the formula for the \( n \)-th term of an arithmetic sequence:

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

where:
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

For this problem:
- \( a = 11 \)
- \( d = -5 \)
- \( n = 65 \)

Substituting the values into the formula:

\[
a_{65} = 11 + (65 - 1) \cdot (-5)
\]
\[
a_{65} = 11 + 64 \cdot (-5)
\]
\[
a_{65} = 11 - 320
\]
\[
a_{65} = -309
\]

The 65th term of the sequence is \(-309\).