tisten NUMBER SENSE Find the sum of the first 22 terms of the sequence \( 17,9,1,-7, \ldots \). The sum

We are given an arithmetic sequence where the first term is \[ a_1 = 17 \] and each subsequent term is obtained by subtracting 8: \[ d = 9 - 17 = -8. \] The sum of the first \(n\) terms of an arithmetic sequence is given by: \[ S_n = \frac{n}{2} \left( 2a_1 + (n-1)d \right). \] For \( n = 22 \), we have: 1. Substitute \( a_1 = 17 \) and \( d = -8 \): \[ S_{22} = \frac{22}{2} \left( 2 \cdot 17 + (22-1)(-8) \right). \] 2. Simplify the expression: \[ S_{22} = 11 \left( 34 + 21(-8) \right). \] 3. Multiply \( 21 \) and \(-8\): \[ 21(-8) = -168. \] 4. Continue simplifying: \[ S_{22} = 11 \left( 34 - 168 \right) = 11 \left( -134 \right). \] 5. Finally, compute the product: \[ S_{22} = -1474. \] The sum of the first 22 terms of the sequence is \(-1474\).