Question 1087946
.
Find the first term & common difference if:


1)  10th term is 35; 15th terms is 55
2)  2nd term is 56 ; 12th term is 16
3)  8th term is 4; 18th term is -96
4)  7th term is -25; 2th term is -45
~~~~~~~~~~~~~~~~~~~~~~


I will solve #1 only. Do the remaining cases following the same pattern.


<pre>
1) 10th term is 35; 15th terms is 55.

   Between the 10-th and 15-th terms, there is the room for 5 (=15-10) common differences d.

   So,  5d = 55 - 35 = 20.  Hence, d = {{{20/5}}} = 4.

   Thus you just found the common difference d = 4.

   Then from {{{a[10]}}} = {{{a[1]}}} + 9*d  you have

             {{{a[1]}}} = {{{a[10]}}} - 9d = 35 - 9*4 = 35 - 36 = -1.


</U>Answer</U>.  {{{a[1]}}} = -1;  d = 4.
</pre>

Make the remaining cases following this pattern.



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>.