Question

1. which explicit formula describes the sequence \\( \\{87, 83.4, 79.8, 76.2, \dots\\} \\)?

\\( a_n = 87 + (n - 1)4 \\)

\\( a_n = 81.6 + (n - 1)(3.6) \\)

\\( a_n = 76.2 + (n - 1)3.6 \\)

\\( a_n = 87 + (n - 1)(-3.6) \\)

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Identify the first term

$$ a_1 = 87 $$

Step 2: Find the common difference

$$ d = 83.4 - 87 = -3.6 $$

Step 3: Write the explicit formula

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

$$ a_n = 87 + (n - 1)(-3.6) $$

Answer:

\( a_n = 87 + (n - 1)(-3.6) \) (the fourth option)