Question
Use the rule to find the 15th term of 75,70,65,60
Answers
GPT-4o mini
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**.
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**.