Q3 of 67 Page 65

Check for an arithmetic progression in the following lists of numbers of any one of these as an arithmetic progression, then find its common difference and also write its next four terms— a, 2a, 3a, 4a ….

Let the arithmetic progression be a1, a2, a3, a4 ……. So here
a2 – a1 = 2a – a = a
a3 – a2 = 3a – 2a = a
a4 – a3 = 4a – 3a = a
For each term difference is same i.e., a. So this sequence is an
arithmetic progression and its common difference is d = a. Next four terms are :
⇒ a5 = a4 + d = 4a + a = 5a
⇒ a6 = a5 + d = 5a + a = 6a
⇒ a7 = a6 + d = 6a + a = 7a
⇒ a8 = a7 + d = 7a + a = 8a


Hence, Yes, d = a, Next four terms are 5a, 6a, 7a, 8a.


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