SOLUTION: The starting salary of a worker in a certain company is 2000000 shillings per annum. If annual increment is 30000 shillings. What is the total amount of money earned by the worker

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Question 1132268: The starting salary of a worker in a certain company is 2000000 shillings per annum. If annual increment is 30000 shillings. What is the total amount of money earned by the worker for twenty years?
Found 3 solutions by ikleyn, MathLover1, greenestamps:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The sequence of annual salaries is arithmetic progression with the first term of 2000000 shillings and the common difference of 30000 shillings.


The problem asks for the sum of the first 20 terms of this progression.


Use the formula for the sum of the first n terms of an AP


    S%5Bn%5D = a%5B1%5D+%2B+a%5B2%5D+%2B+a%5B3%5D+%2B+ellipsis+%2B+a%5Bn%5D = %28a%5B1%5D+%2B+%28n-1%29%2Ad%2F2%29%2An = %282000000+%2B+%2820-1%29%2A%2830000%2F2%29%29%2A20 = 4570000 shillings.    ANSWER

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


Answer by MathLover1(20850) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The yearly salaries form an arithmetic sequence. The sum is

(number of years) times (average salary)

Because the salaries form an arithmetic sequence, the average salary is the average of the first and last year's salaries.

first year salary: 2000000
20th year salary: 2000000 + 19(30000) = 2570000

Total salary for 20 years:

20%2A%28%282000000%2B2570000%29%2F2%29+=+10%2A4570000+=+45700000