Question

Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After his seventh load of logs, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function.

an = 8 + 6(n − 1)
an = 62 + 6(n − 1)
an = 8 + 9(n − 1)
an = 62 + 9(n − 1)

Answer 1

an = 8 + 9(n − 1)

Explanation:

We assume that Max is adding the same number of logs to his stack on each load after the first, so the sequence of stack counts is an arithmetic sequence.

The given sequence has ...

a1 = 8

a7 = 62

The general term of an arithmetic sequence has the formula ...

an = a1 +d(n -1)

where a1 is the first term and d is the common difference between terms.

__

You can immediately reject the 2nd and 4th answer choices, because they have a first term value of 62. You can determine the appropriate choice by solving the general equation for d, or by substituting n=7 into the offered choices to see which fits.

Find the equation:

an = a1 +d(n -1)

62 = 8 +d(7 -1)

54 = 6d

9 = d

so, the equation is an = 8 +9(d -1) . . . . . matches 3rd choice

Try the answers:

substitute n=7 into the equations and see if you get a7=62.

1st choice: a7 = 8 + 6(7 -1) = 8 +36 = 44 ≠ 62

3rd choice: a7 = 8 +9(7 -1) = 8 +54 = 62 . . . . correct choice