Write an expression for the arithmetic sequence whose 2 nd term is 8 and whose 5 th term is 17 \( a_{n}=17-3 n \) \( a_{n}=8+3 n \) \( a_{n}=3 n+2 \) \( a_{n}=3 n+5 \)
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To find the expression for the arithmetic sequence, we first need to determine the common difference. Since we know the 2nd term \( a_2 \) is 8 and the 5th term \( a_5 \) is 17, we can set up the equations. The common difference \( d \) can be calculated as: 1. \( a_5 = a_2 + 3d \implies 17 = 8 + 3d \) 2. Solving for \( d \) gives \( d = 3 \). Now, the first term \( a_1 \) can be found using the 2nd term: - \( a_2 = a_1 + d \) \(\implies 8 = a_1 + 3\) \(\implies a_1 = 5 \). Now that we have the first term \( a_1 = 5 \) and the common difference \( d = 3 \), the general term formula for the arithmetic sequence can be written as: \[ a_n = a_1 + (n-1)d \\ a_n = 5 + (n-1)3 \\ a_n = 3n + 2. \] The correct expression is \( a_{n}=3 n+2 \). So, the right answer is \( a_{n}=3 n+2 \).
