SOLUTION: which term of the arithmetic sequences: 3x - 4 ; 4x - 3; 7x - 6 ;.....is equals to 5x + 4

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Question 1140958: which term of the arithmetic sequences: 3x - 4 ; 4x - 3; 7x - 6 ;.....is equals to 5x + 4
Answer by ikleyn(52794) About Me  (Show Source):
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            This problem is to be solved in two steps.


STEP 1.   Find  x. 

Since the sequence is an arithmetic progression, the difference  a%5B3%5D-a%5B2%5D  is  the same as the difference  a%5B2%5D-a%5B1%5D.


It gives an equation to find x


    (7x-6) - (4x-3) = (4x-3) - (3x-4),    or, simplifying

    3x - 3          = x + 1

    3x - x          = 1 + 3

    2x              = 4

     x              = 4/2 = 2.


So,  a%5B1%5D = 3x - 4 = 3*2 - 4 = 2  and  d = a%5B2%5D-a%5B1%5D = (4x-3) - (3x-4) = (4*2-3) - (3*2-4) = 5 - 2 = 3.


The progression is  2, 5, 8, . . .


STEP 2.   Which term ? 

Now the question is " which term is equal to 5*2 + 4 = 14 ? " 


It is easy:  2, 5, 8, 11, 14.


ANSWER.  The 5-th term, a%5B5%5D = 14.