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Decide whether the given sequence 24, 17, 10, 3, ...... is an A.P.? If yes find its common term (tn) - Algebra

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Sum

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

Concept: General Term of an Arithmetic Progression
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