Question 1197283
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Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is - 4.
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<pre>
Between the 3rd term and 6th term, there are 3 gaps of equal size on the number line.

The size of each gap is  {{{(20 - (-4))/3}}} = {{{24/3}}} = 8 units.


Hence, the common difference of this arithmetic sequence is d = -8 
    (it is exactly the gap size, but the sequence is decreasing, so the common difference is negative).


Next, the 1st term is 2 gaps backward from the 3rd term,
so, the 1st term is  {{{a[1]}}} = 20 - 2*(-8) = 20 + 16 = 36.


<U>ANSWER</U>.  First term of this arithmetic progression is 36.


<U>CHECK</U>.  {{{a[6]}}} = {{{a[1] + 5*d}}} = 36 + 5*(-8) = 36 - 40 = -4.   ! correct !
</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.