SOLUTION: 2x-4;x+5 and 3x-1 are the first three terms of an arithmetic sequence.(I) show that x=5 and write the first three terms of the sequence

Question 1070563: 2x-4;x+5 and 3x-1 are the first three terms of an arithmetic sequence.(I) show that x=5 and write the first three terms of the sequence
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

You are given

 = 2x-4;   = x+5;    = 3x-1.


Since they are three consecutive terms of an arithmetic progression,

 =    (each side is the common difference of the progression).


It gives you an equation


(x+5) - (2x-4) = (3x-1) - (x+5).


Simplify and solve for x:

-x + 9 = 2x - 6,

9 + 6 = 2x + x  --->  15 = 3x   --->  x =  = 5.


The three terms of the sequence are 

 = 2*5-4 = 6;

 = 5 + 5 = 10;

 = 3*5-1 = 14.

Solved.

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".

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