Question

n for each sequence before finding the nth term. 8. {8,16,24,32,...} what is the 107th term?

Explanation:

Step1: Identify sequence type

The sequence \( \{8, 16, 24, 32, \dots\} \) is arithmetic. First term \( a_1 = 8 \), common difference \( d = 16 - 8 = 8 \).

Step2: Arithmetic sequence formula

The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \).

Step3: Substitute values for \( n = 107 \)

Substitute \( a_1 = 8 \), \( d = 8 \), \( n = 107 \) into the formula:
\( a_{107} = 8 + (107 - 1) \times 8 \)
Simplify: \( a_{107} = 8 + 106 \times 8 = 8 + 848 = 856 \).

Answer:

\( 856 \)