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Check whether the following sequences are in A.P. (i) a - 3, a - 5, a -7,...

Check whether the following sequences are in A.P.
(i) a - 3, a - 5, a -7,...
Solution :
d = t2 - t1
d = (a - 5) - (a - 3)
  =  a - 5 - a + 3
d  = -2
d = t3 - t2
d = (a - 7) - (a - 5)
  =  a - 7 - a + 5
d  = -2
Since the common difference area same, the given sequence is an arithmetic progression.