Q.151. Arithmetical Progression.

Question 151.
In a given AP, if the pth term is q, and the qth term is p show that the nth term is (p+q-n).?

Answer 151.
Let the A.P. be given by
a, a+d, a+2d, a+3d,.....
q = a + (p -1)d ... ( 1 )
p = a + (q -1)d ... ( 2 )

Subtracting ( 2 ) from ( 1 ),
q - p = (p - q)d
=> d = -1
Putting d = -1 in ( 1 ), a = p + q - 1
nth term = a + (n - 1)d
 Substituting the values of a and d,
nth term = p + q - 1 + (n -1)(-1) = p + q - n.

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