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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)
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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