SOLUTION: The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th term

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Question 1091923: The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th term
Found 2 solutions by ikleyn, Fombitz:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th term
~~~~~~~~~~~~~~~~~ 

 = 8 = .   (1)   ( is the first term of the AP)

 = 2 = .   (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 =  = -2.


Now  =  =  +  =  = 8 + 27*(-2) = 8 - 54 = -46.


Answer.   = -46.

Solved. 

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

n    
---------------

1	         I do not need the terms  and ,
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


-------------------
There is a bunch of lessons on arithmetic progressions in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

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.



Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

So,

1.
and

2.
Subtract 1 from 2,



Now use either equation to solve for .
Then solve for,
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