Question

If 4th term of an ap is 64 and its 54th term is -61, then its common difference is

Answer 1

An=a+(n-1)d                          

A4=a+3d                                A54=a+53d

64=a+3d      (eq.1)                  -61=a+53d    (eq.2)

Subtracting eq.1 and eq.2, we get

 64=a+3d

 61=-a-53d          (changing the signs)

125=-50d

=>d= -125/50

=>d= -2.5

.:The common difference is -2.5.