Problem
The given table of values represents terms in an arithmetic sequence. \( \begin{array}{ccccc}n & 1 & 2 & 3 & 4 \\ T_{n} & 9 & 17 & 25 & 33\end{array} \) Identify \( d \), the common difference between consecutive terms. \( d=8 \) Write a simplified expression for the general \( n \)th term of the sequence, \( T_{n} \). \( T_{n}=9+(n-1) 8 \) \( T_{n}=1+8 n \) Find the 13 th term of the sequence. \[ T_{13}=\text { Enter your next step here } \]
Solution
Step 1 ：\( T_{n}=1+8 n \)
Step 2 ：\( T_{13} = 1 + 8(13) \)
Step 3 ：\( T_{13} = 1 + 104 \)
Step 4 ：\( T_{13} = 105 \)
