Question 1193591
.
Find the sum of this series that is not arithmetic or geometric,
1+2+4+5+7+8....+95+97+98
can someone help, a few of us have been trying to figure this out, 
our teacher said its solvable but I don't even know where to start, thankyou
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The major problem with your post is that it is  BAD  STYLE  presenting a  Math task.



Actually,  in your post the problem is not posed as a  Math problem.

The reader should guess what this sequence/series is.

When a reader should guess what the author wants to say,  it is just not a  Math problem.



So,  I will re-formulate it to present it in a way,  as it  SHOULD  be presented.


<pre>
    +------------------------------------------------------------------------+
    |  In the sequence of 99 first natural numbers from 1 to 99 inclusive,   |
    |  each third term is removed. Find the sum of remaining numbers.        |
    +------------------------------------------------------------------------+
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Now it is normal Math entertainment problem.


<pre>
For the solution, the reader should know that the sum of the first n natural numbers is {{{(n*(n+1))/2}}}.

It is one of the basic facts about arithmetic progressions.


If you don't know it, you may derive this formula, but then the problem itself is not an entertainment - it is just 
full size study piece of knowledge.


So, to keep this style of entertainment problem, I will assume that you know this formula.


If so, then the entire problem is two easy steps.


First, the sum of natural numbers from 1 to 99 is  {{{(99*(99+1))/2}}} = {{{(99*100)/2}}} = 99*50 = 4950.


From it, we should subtract the sum of all "removed" terms, which is

    3 + 6 + 9 + . . . + 96 + 99 = 3*(1 + 2 + 3 + . . . + 32 + 33).


In the parentheses, we have the sum of the first 33 natural numbers, which is  {{{(33*(33+1))/2}}} = 33*17 = 561.


Now your  <U>ANSWER</U>  is this difference  4950 - 3*561 = 3267.
</pre>

Solved &nbsp;&nbsp;(keeping the style of an entertainment problem).


-------------------


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.



<H3>Also, did your mother or other relatives teach you to thank those who help you ?</H3>