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A man is able to save 50naira of his salary in a particular year.
After every year he saved 20naira more the preceding year.
How long does it take him to save 4370naira
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This problem introduces an arithmetic progression with the first term a= 50
and the common difference d = 20.
Then the problem asks you to determine the number of terms such that their sum is 4370.
Use the formula for the sum of arithmetic progression
= .
In this problem, it takes the form
=
and gives you this equation
4370 = (50 + 10(n-1))*n,
Reduce the common factor of 10 in both sides and simplify step by step
437 = 5n + n^2 - n
n^2 + 4n - 437 = 0.
Solve using the quadratic formula
= = .
There are two roots, one positive and the other negative.
Naturally, you want only positive number of terms n = = = 19.
ANSWER. It will take him 19 months to get his goal.
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.