Question 1198930
.
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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<pre>
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

    {{{S[n]}}} = {{{(a + (n-1)*d/2)*n}}}.


In this problem, it takes the form

    {{{S[n]}}} = {{{(50 + (n-1)*10)*n}}}


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

    {{{n[1,2]}}} = {{{(-4 +- sqrt(4^2+4*437))/2}}} = {{{(-4 +- 42)/2}}}.


There are two roots, one positive and the other negative.

Naturally, you want only positive number of terms  n = {{{(-4 + 42)/2}}} = {{{38/2}}} = 19.


<U>ANSWER</U>.  It will take him 19 months to get his goal.
</pre>

Solved.


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For introductory lessons on arithmetic progressions see 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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



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.