SOLUTION: find the twentieth term of the arithmetic sequence in which t4 = a and t12=b?

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Question 1028709: find the twentieth term of the arithmetic sequence in which t4 = a and t12=b?
Answer by ikleyn(52788) About Me  (Show Source):
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find the twentieth term of the arithmetic sequence in which t4 = a and t12=b?
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In other words, find the term  t%5B20%5D  of an AP,  if you are given that
t%5B4%5D = a   and  t%5B12%5D = b.


You have 

t%5B4%5D = t%5B1%5D+%2B+3d = a      and
t%5B12%5D = t%5B1%5D+%2B+11d = b.

Consider  2%2At%5B12%5D - t%5B4%5D = 2%2A%28t%5B1%5D+%2B+11d%29+-+%28t%5B1%5D%2B3d%29 =  2t%5B1%5D+%2B+22d+-+t%5B1%5D+-+3d = t%5B1%5D+%2B+19d.

The right side is exactly  t%5B20%5D.

Therefore,  t%5B20%5D = 2b - a.

Answer.  t%5B20%5D = 2b - a.