Question

A house worth $350,00 when purchased was worth $335,000 after the first year and $320,000 after the second year. Assume the economy does not pick up and this trend continues.

(is this an arithmetic or geo sequence?)

Write an explicit formula for the sequence.

Answer 1

Answer: Arithmetic Sequence

The nth term formula is  $a_n = -15,000n + 365,000$

Delete the commas if needed.

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Explanation:

Subtract each adjacent term like this

• term2 - term1 = (335,000) - (350,000) = -15,000
• term3 - term2 = (320,000) - (335,000) = -15,000

Each time we get -15,000 which is the common difference and helps show we have an arithmetic sequence.

The nth term formula can be found following these steps.

$a_n = a + d(n-1)\\\\a_n = 350,000 + (-15,000)(n-1)\\\\a_n = 350,000 - 15,000n + 15,000\\\\a_n = -15,000n + 365,000$

If we plugged in n = 1, then we'd get,

$a_n = -15,000n + 365,000\\\\a_1 = -15,000(1) + 365,000\\\\a_1 = -15,000 + 365,000\\\\a_1 = 350,000$

Showing the first term is $350,000 which is the initial value of the house.

I'll let you try the other values of n.

Plugging in n = 2 would lead to $a_2 = 335,000$

Plugging in n = 3 would lead to $a_3 = 320,000$