Questions: 1 - Introduction to Arithmetic Sequences LEARNING OBJECTIVE: Calculate the value of the nth term or the term number that has a specific value in an arithmetic sequence. If the formula for an arithmetic sequence is an=11+6(n-1), then what term in the sequence is the value 107 ? a.) 17th term b.) 15th term C.) 16th term d.) 18th term

1 - Introduction to Arithmetic Sequences
LEARNING OBJECTIVE: Calculate the value of the nth term or the term number that has a specific value in an arithmetic sequence.

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

Transcript text: 1 - Introduction to Arithmetic Sequences LEARNING OBJECTIVE: Calculate the value of the $n$th term or the term number that has a specific value in an arithmetic sequence. 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.) 17th term b.) 15th term C.) 16th term d.) 18th term

Solution

Solution Steps

To find the term number $ n $ in the arithmetic sequence where the term value is 107, we can set up the equation $ a_n = 107 $ and solve for $ n $. Given the formula for the arithmetic sequence $ a_n = 11 + 6(n-1) $, we substitute 107 for $ a_n $ and solve for $ n $.

Step 1: Set Up the Equation

Given the formula for the arithmetic sequence: \[ a_n = 11 + 6(n-1) \] We need to find the term number $ n $ when the term value $ a_n $ is 107. Set up the equation: \[ 107 = 11 + 6(n-1) \]

Step 2: Simplify the Equation

First, subtract 11 from both sides: \[ 107 - 11 = 6(n-1) \] \[ 96 = 6(n-1) \]

Step 3: Solve for $ n $

Next, divide both sides by 6: \[ \frac{96}{6} = n-1 \] \[ 16 = n-1 \]

Finally, add 1 to both sides to solve for $ n $: \[ n = 16 + 1 \] \[ n = 17 \]