A middle school mathematics teacher except a teaching position that pays 40,000 per year, each year the expected raise is $2000. How much total money with this teacher and teaching middle school math Mathematics over the first 30 years?

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  $2,070,000

Step-by-step explanation:

The series of salaries has a first term of $40,000 and a common difference of $2,000. The sum of them is given by the formula ...

  Sn = (2a1 +d(n -1))(n/2)

where a1 is the first term of the series, d is the common difference, and n is the number of terms.

In this problem, we have ...

  a1 = 40,000; d = 2,000; n = 30

so the sum is ...

  S30 = (2(40,000) +2,000(30 -1))(30/2) = (80,000 +58,000)(15)

  S30 = 2,070,000

The teacher will earn $2,070,000 over 30 years on this salary schedule.

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