Question 1084122
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<pre>
{{{a[3]}}} = {{{a[1]+2d}}} = 16,   (1)

{{{a[6]}}} = {{{a[1]+5d}}} = 34.   (2)


====>  3d = 34 - 16 = 18  ====>  d = {{{18/3}}} = 6.


Then {{{a[1]}}} = {{{a[3] - 2*d}}} = 16 - 2*6 = 4.


Then {{{a[20]}}} = {{{a[1] + 19*d}}} = 4 + 19*6 = 118.


Then the sum of the first 20 terms is

{{{S[20]}}} = {{{(a[1]+a[20])/2}}}.{{{20}}} = {{{(4 + 118)/2}}}.{{{20}}} = 1220.
</pre>

Solved.



There is a bunch of lessons on arithmetic progressions in this site:

&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>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/One-characteristic-property-of-arithmetic-progressions.lesson>One characteristic property of arithmetic progressions</A>

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



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>.