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.