If the formula for an arithmetic sequence is \( a_{n}=11+6(n-1) \), then what term in the sequence is the value 107 ? a.) 15 th term b.) 16 th term c.) 17 th term d.) 18 th term

To find out which term in the sequence gives the value 107, we can set \( a_{n} \) equal to 107 and solve for \( n \): \[ 11 + 6(n-1) = 107 \] Subtract 11 from both sides: \[ 6(n-1) = 96 \] Now, divide both sides by 6: \[ n-1 = 16 \] Finally, add 1 to both sides: \[ n = 17 \] Thus, the value 107 is the 17th term in the sequence. The answer is c.) 17th term. If you want a quick way to verify your answer, plug \( n = 17 \) back into the formula: \[ a_{17} = 11 + 6(17-1) = 11 + 6 \times 16 = 11 + 96 = 107. \] And there you have it, 107 pops up perfectly in the sequence!