Question 1091923
.
The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th term
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<pre>
{{{a[3]}}} = 8 = {{{a[1] + 2d}}}.   (1)   ({{{a[1]}}} is the first term of the AP)

{{{a[6]}}} = 2 = {{{a[1] + 5d}}}.   (2)   (d is the common difference of the AP)


Subtract eqn(1) from eqn(2). You will get

5d - 2d = 2 - 8,   or   3d = -6.   Hence, d = {{{-6/3}}} = -2.


Now {{{a[30]}}} = {{{a[1] + 29d}}} = {{{(a[1]+2d)}}} + {{{27d}}} = {{{a[3] + 27d}}} = 8 + 27*(-2) = 8 - 54 = -46.


<U>Answer</U>.  {{{a[30]}}} = -46.
</pre>

Solved.


<pre>
To confirm my solution, I prepared this Table in Excel on my computer.

n    {{{a[n]}}}
---------------

1	         I do not need the terms {{{a[1]}}} and {{{a[2]}}},
2	         so I left these cells empty.
3	8
4	6
5	4
6	2
7	0
8	-2
9	-4
10	-6
11	-8
12	-10
13	-12
14	-14
15	-16
16	-18
17	-20
18	-22
19	-24
20	-26
21	-28
22	-30
23	-32
24	-34
25	-36
26	-38
27	-40
28	-42
29	-44
30	-46
</pre>


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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>.


Save the link to this textbook


https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.