Question
Find the 80th term of the following sequence.
9 comma 18 comma 27 comma ...
Question content area bottom
Part 1
a 80equals
enter your response here
9 comma 18 comma 27 comma ...
Question content area bottom
Part 1
a 80equals
enter your response here
Answers
GPT-4o mini
The given sequence is 9, 18, 27, ...
This is an arithmetic sequence where the first term \( a_1 = 9 \) and the common difference \( d = 18 - 9 = 9 \).
The formula for the \( n \)th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
To find the 80th term (\( a_{80} \)), we can substitute \( n = 80 \), \( a_1 = 9 \), and \( d = 9 \) into the formula:
\[
a_{80} = 9 + (80 - 1) \cdot 9
\]
Calculating this step by step:
1. Calculate \( 80 - 1 \):
\[
80 - 1 = 79
\]
2. Multiply \( 79 \) by \( 9 \):
\[
79 \cdot 9 = 711
\]
3. Add this result to \( 9 \):
\[
a_{80} = 9 + 711 = 720
\]
Thus, the 80th term of the sequence is:
\[
\boxed{720}
\]
This is an arithmetic sequence where the first term \( a_1 = 9 \) and the common difference \( d = 18 - 9 = 9 \).
The formula for the \( n \)th term of an arithmetic sequence is given by:
\[
a_n = a_1 + (n - 1) \cdot d
\]
To find the 80th term (\( a_{80} \)), we can substitute \( n = 80 \), \( a_1 = 9 \), and \( d = 9 \) into the formula:
\[
a_{80} = 9 + (80 - 1) \cdot 9
\]
Calculating this step by step:
1. Calculate \( 80 - 1 \):
\[
80 - 1 = 79
\]
2. Multiply \( 79 \) by \( 9 \):
\[
79 \cdot 9 = 711
\]
3. Add this result to \( 9 \):
\[
a_{80} = 9 + 711 = 720
\]
Thus, the 80th term of the sequence is:
\[
\boxed{720}
\]