Answer:
a) The formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
b) [tex]a_7 = 49,000[/tex]
Step-by-step explanation:
Note that the difference between any two consecutive terms in the sequence is always equal to $3,000
[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]
Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.
The explicit formula for an arithmetic sequence is:
[tex]a_n = a_1 +d(n-1)[/tex]
Where d is the common difference between the consecutive terms of the sequence
[tex]d = -3,000[/tex]
[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]
n represents the number of years since the house was purchased
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
a) Then the formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
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b) Now we can use the formula to find the price of the house after 7 years
[tex]a_7 = 67,000 -3,000(7-1)[/tex]
[tex]a_7 = 67,000 -3,000(6)[/tex]
[tex]a_7 = 49,000[/tex]
