Question 1162919
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<pre>

The sum of the first 4 terms is  {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}}.


The sum of the next 4 terms is  {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} + {{{a[8]}}}.


Each difference  {{{a[5]-a[1]}}},  {{{a[6]-a[2]}}},  {{{a[7]-a[3]}}}  and  {{{a[8]-a[4]}}}  is equal to 4d,

where d is the common difference of the AP.



Therefore,  4*(4d) = 74 - 26,   or  16d = 48;  hence, d = 48/16 = 3.



Next,  26 = 4a + (1+2+3)d = 4a + 6*3 = 4a + 18,  which implies


       4a = 26 - 18 = 8.


<U>Answer</U>.  The first term of the AP is 8/4 = 2;  the common difference is 3.
</pre>

Solved.


The goal of this problem is to teach you manipulate with AP terms quickly and informally.


It is a simple problem; so, the method of its solution should be adequately simple.


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On arithmetic progressions, see the lessons 

&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/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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Calculating-partial-sums-of-arithmetic-progressions.lesson>Calculating partial sums of arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Finding-number-of-terms-of-an-arithmeti--progression.lesson>Finding number of terms of an arithmetic progression</A> 

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

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