Question

1. eleri mows grass in her neighborhood. she charges \\$35 per yard. but she decreases her price by \\$3 each time she mows a yard for the same customer. a customer hires eleri to mow her lawn for the 8th time. which explicit formula describes how much she charges for the \\(n\\)th time?

\\(a_n = 35 + (n - 1)(-3)\\)
\\(a_n = 24 - (n + 1)(-3)\\)
\\(a_n = 30 + (n - 1)(8)\\)
\\(a_n = 35 - (n - 1)(3)\\)

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Identify the sequence parameters

The problem describes an arithmetic sequence where:

• The first term (the charge for the first yard) is \( a_1 = 35 \).
• The charge decreases by \(\$3\) each subsequent time, which gives a common difference of \( d = -3 \).

Step 2: Apply the explicit formula

The explicit formula for an arithmetic sequence is:

$$ a_n = a_1 + (n - 1)d $$

Substitute \( a_1 = 35 \) and \( d = -3 \):

$$ a_n = 35 + (n - 1)(-3) $$

Step 3: Match with the given options

For the 8th time (\( n = 8 \)), the formula is written as:

$$ a_8 = 35 + (n - 1)(-3) $$

This matches the first option.

Answer:

\( a_8 = 35 + (n - 1)(-3) \)