Question 1140958
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            This problem is to be solved in two steps.



<U>STEP 1</U>.  &nbsp;&nbsp;Find &nbsp;x.


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Since the sequence is an arithmetic progression, the difference  {{{a[3]-a[2]}}}  is  the same as the difference  {{{a[2]-a[1]}}}.


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[1]}}} = 3x - 4 = 3*2 - 4 = 2  and  d = {{{a[2]-a[1]}}} = (4x-3) - (3x-4) = (4*2-3) - (3*2-4) = 5 - 2 = 3.


The progression is  2, 5, 8, . . . 
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<U>STEP 2</U>.  &nbsp;&nbsp;Which term ?


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


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


<U>ANSWER</U>.  The 5-th term, {{{a[5]}}} = 14.
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