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Marquis begins a career making $53,000 per year. Each year, he is to receive a $1,600 raise. After 25 years, how much total money will Marquis have earned from this career?

$1,792,000
$1,805,000
$1,844,975
$1,845,000

Respuesta :

morgaine816
First, you find what he will be making in the 25th year:

[tex] a_{n} = a_{1} +(n-1)d[/tex]
[tex] a_{25}= 53000+(25-1)1600 [/tex]
               = 53000+(24)1600
               =53000+38400=91400

So in year 25 he was making $91400
To find the sum of all of that the formula is [tex] S_{n} = \frac{n}{2}( a_{1} + a_{n)} [/tex]
In this case we are trying to find [tex] S_{25} [/tex] and n=25, [tex] a_{1} =53000 [/tex] and [tex] a_{25} = 91400[/tex] so we just plug it in
[tex] S_{25}= \frac{25}{2}(53000+91400)= \frac{25}{2} (144400) =1805000[/tex]

Hope that helps

After 25 years, the total money will Marquis have earned from this career is $1,805,000. Then the correct option is B.

What is a series?

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

Marquis begins a career-making $53,000 per year. Each year, he is to receive a $1,600 raise.

First, you find what he will be making in the 25th year:

[tex]\rm a_n = a_1 +(n-1)d\\\\a_{25} = 53000 +(25-1)1600\\\\a_{25} = 91400[/tex]

Then the sum will be

[tex]\rm S_n = \dfrac{n}{2} \times (a_1 + a_n) \\\\S_{25} = \dfrac{25}{2} \times (53000+ 91400)\\\\S_{25} = 1,805,000[/tex]

More about the series link is given below.

https://brainly.com/question/10813422

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