SOLUTION: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the 20th term?

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Question 1159788: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the 20th term?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let "a" be the first term of the AP, and let "d" be its common difference.


Then from the condition you have these two equations


    3*(a+d) = a + 4d      (1)    (which means   =  )

    a + 2d  = 10          (2)    (which means   = 10 )


From equation (1)

    3a + 3d = a + 4d

     2a     = d           (3)


From equation (2)

     2a + 4d = 20,


and substituting (replacing) here 2a = d  from (3), you get

    d  + 4d = 20,

    5d      = 20,

     d      = 20/5 = 4.



Now from equation (2)

    a = 10-3d = 10-2*4 = 2.


So, the progression has the first term  a= 2  and  the common difference  d= 4.


In particular, the 20-th term is

     = a + 19*d = 2 + 19*4 = 78.      ANSWER

Solved.

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On arithmetic progressions, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Chocolate bars and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
    - Calculating partial sums of arithmetic progressions
    - Finding number of terms of an arithmetic progression
    - Advanced problems on arithmetic progressions
    - Problems on arithmetic progressions solved MENTALLY
in this site.

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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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the 20th term?
           

                   

 

 ------ Substituting 2a1 for d

      

         

       ------ Substituting 2 for a1

      d, or common difference = 4  

, and so:  

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