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Question
Decide whether the given sequence 24, 17, 10, 3,...... is an A.P.? If yes find its common term (tn).
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Solution
The given sequence is 24, 17, 10, 3,......
Here, t1 = 24, t2 = 17, t3 = 10, t4 = 3
∴ t2 – t1 = 17 – 24 = – 7
t3 – t2 = 10 – 17 = – 7
t4 – t3 = 3 – 10 = – 7
∴ t2 – t1 = t3 – t2 = ... = – 7 = d = constant
The difference between two consecutive terms is constant.
∴ The given sequence is an A.P.
tn = a + (n – 1)d
= 24 + (n – 1)(– 7)
= 24 – 7n + 7
= 31 – 7n
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