11-5 65th term

1 answer

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 \(-309\).