Write an expression for the arithmetic sequence whose 2 nd term is 8 and whose 5 th term is 17 \( a_{n}=17-3 n \) \( a_{n}=8+3 n \) \( a_{n}=3 n+2 \) \( a_{n}=3 n+5 \)

To find the arithmetic sequence where the 2nd term is 8 and the 5th term is 17, let's use the general formula for an arithmetic sequence: \[ a_n = a + (n-1)d \] where: - \( a \) is the first term, - \( d \) is the common difference, - \( n \) is the term number. **Given:** 1. The 2nd term (\( a_2 \)) is 8: \[ a + d = 8 \] 2. The 5th term (\( a_5 \)) is 17: \[ a + 4d = 17 \] **Steps to Solve:** 1. **Subtract the first equation from the second to eliminate \( a \):** \[ (a + 4d) - (a + d) = 17 - 8 \\ 3d = 9 \\ d = 3 \] 2. **Find the first term (\( a \)) using \( d = 3 \) in the first equation:** \[ a + 3 = 8 \\ a = 5 \] 3. **Write the general formula for the sequence:** \[ a_n = a + (n-1)d \\ a_n = 5 + (n-1) \times 3 \\ a_n = 5 + 3n - 3 \\ a_n = 3n + 2 \] **Therefore, the arithmetic sequence is:** \[ a_{n} = 3n + 2 \] **Answer:** \( a_{n}=3 n+2 \)