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:
-
Calculate \( 80 - 1 \): \[ 80 - 1 = 79 \]
-
Multiply \( 79 \) by \( 9 \): \[ 79 \cdot 9 = 711 \]
-
Add this result to \( 9 \): \[ a_{80} = 9 + 711 = 720 \]
Thus, the 80th term of the sequence is:
\[ \boxed{720} \]
9 answers