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

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

           

                   

 

 ------ Substituting 2a1 for d

      

         

       ------ Substituting 2 for a1

      d, or common difference = 4  

, and so: