SOLUTION: For a given arithmetic sequence, the 42nth term, a42, is equal to 194, and the 88th term, a88, is equal to 424. Find the value of the 10th term, a10.

 = a + 41*d = 194.    (1)

 = a + 87*d = 424.    (2)


The unknown "a" is the first term, and the unknown "d" is the common difference of the AP.


Thus you have the system of 2 linear equations in 2 unknown, so it is solvable.


The easiest way to solve it is to subtract equation (1) from equation (2). You will get

    87d - 41d = 424 - 194  

    46d       = 230

      d       = 230/46 = 5.


Then from equation (1),  a = 194 - 5*41 = -11.


Now you know EVERYTHING about your AP.  In particular,

     = a + 5*9 = -11 + 45 = 34.      ANSWER