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3 years ago

6

A car was originally purchased in January 2010 for 27000 dollars. The car depreciates at a rate of 18% every year.

1 answer:

Maksim231197 [3]3 years ago

5 0

Answer:

Number of year(n) = 3.4 year (Approx)

Step-by-step explanation:

Given:

Purchase value of car = $27,000

Depreciation rate per year (d) = 18% = 0.18

Future price = half of its original value = $27,000 / 2 = $13,500

Find:

Number of year(n) = ?

Computation:

$Future price =Purchase value(1-d)^n\\\\13,500=27,000(1-0.18)^n\\\\0.5=(0.82)^n\\\\n=3.444(Approx)$

Number of year(n) = 3.4 year (Approx)

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What is the sum of the first 37 terms of the arithmetic sequence?

lidiya [134]

Answer:

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Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

The sum of the first n terms of an arithmetic sequence is given by:

$S_{n} = \frac{n(a_{1} + a_{n})}{2}$

In this question:

$a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6$

We want the sum of the first 37 terms, so we have to find $a_{37}$

$a_{n} = a_{1} + (n-1)*d$

$a_{37} = a_{1} + (36)*d$

$a_{37} = -27 + 36*6$

$a_{37} = 189$

Then

$S_{37} = \frac{37(-27 + 189)}{2} = 2997$

The sum of the first 37 terms of the arithmetic sequence is 2997.

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