Ask a Teacher

Search



The second term of an AP IS (x-y)and the fifth term is (x+y)then it's first term is?
We know that the nth term of an A.P. is given by
            an=a+(n-1)d, where a is the first term and d is the common difference
given,          a2 = x-y
    ? a+(2-1)d = x-y
    ?         a+d = x-y -----(1)
 
also,         a5 = x+y
    ? a+(5-1)d = x+y
    ?     a+4d = x+y---------(2)

(2)-(1) gives
          3d = 2y
           d = 2y/3

substituting the value of d in (1)
  a+2y/3 = x-y
         a = x-y-2y/3
         a = 3x-3y-2y/3
 i.e.,   a = 3x-5y/3