Use the rule to find the 15th term of 75,70,65,60

1 answer

The sequence you provided is: 75, 70, 65, 60.

To find the pattern, we observe the differences between consecutive terms:

  • 75 to 70: decrease of 5
  • 70 to 65: decrease of 5
  • 65 to 60: decrease of 5

The sequence is an arithmetic sequence where the first term \( a = 75 \) and the common difference \( d = -5 \).

The \( n \)-th term of an arithmetic sequence can be found using the formula:

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

To find the 15th term (\( a_{15} \)):

\[ a_{15} = 75 + (15-1) \cdot (-5) \] \[ a_{15} = 75 + 14 \cdot (-5) \] \[ a_{15} = 75 - 70 \] \[ a_{15} = 5 \]

Therefore, the 15th term of the sequence is 5.