The salary scale for an officer starts at $1,700,000 .A rise of $4000 is given at the end of each share . Find the total amount of money the officer will earn in 14 years

9514 1404 393

  $24,164,000

Step-by-step explanation:

The yearly salaries form an arithmetic sequence with a first term of 1700000 and a common difference of 4000.

The sum of n terms of an arithmetic sequence with first term a1 and common difference d is ...

  Sn = (2a1 +d(n -1))(n/2)

For the given numbers, the sum of 14 years' salaries will be ...

  S14 = (2·1,700,000 +4,000(14 -1))(14/2) = 24,164,000

The officer will earn $24,164,000 in a 14-year period.

Clearly, we can see that salary of the officer is in form of Arithmetic progession, where :

And we have to find total salary i.e.

Now, we know that :

By substituting values :

Hence, the total amount of money the officer will earn in 14 years is $ 24,164,000.

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