a new dump truck costs $75,000. it has a useful life of 10 years and a salvage value of $12,000. which…

a new dump truck costs $75,000. it has a useful life of 10 years and a salvage value of $12,000. which equation is the explicit formula for the sequence that represents this assets depreciation?\n$a_n = 1,200+(n - 1)(-7,500)$\n$a_n = 75,000+(n - 1)(-6,300)$\n$a_n = 1,200+(n - 1)(-6,300)$\n$a_n = 75,000+(n - 1)(-1,200)$

a new dump truck costs $75,000. it has a useful life of 10 years and a salvage value of $12,000. which equation is the explicit formula for the sequence that represents this assets depreciation?\n$a_n = 1,200+(n - 1)(-7,500)$\n$a_n = 75,000+(n - 1)(-6,300)$\n$a_n = 1,200+(n - 1)(-6,300)$\n$a_n = 75,000+(n - 1)(-1,200)$

Answer

Explanation:

Step1: Calculate total depreciation

The initial cost of the dump - truck is $C = 75000$ and the salvage value is $S=12000$. The total depreciation over 10 years is $D = C - S=75000 - 12000=63000$.

Step2: Calculate annual depreciation

The annual depreciation $d$ (the common difference of the arithmetic - sequence representing depreciation) is $d=\frac{D}{n}=\frac{63000}{10}=6300$. The first - term $a_1$ of the sequence representing the value of the asset at the start of the first year is the initial cost, $a_1 = 75000$. The explicit formula for an arithmetic sequence is $a_n=a_1+(n - 1)d$. Substituting $a_1 = 75000$ and $d=-6300$ (negative because the value of the asset is decreasing), we get $a_n = 75000+(n - 1)(-6300)$.

Answer:

$a_n = 75000+(n - 1)(-6300)$