# Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer. - Mathematics

Sum

Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.

#### Solution

Let 0 be the nth term of given AP i.e., an = 0.

Given that, first term a = 31

Common difference, d = 28 – 31 = – 3

The nth terms of an AP, is

a_n = a + (n - 1)d

⇒ 0 = 31 + (n - 1)(-3)

⇒ 3(n - 1) = 31

⇒ n - 1 = 31/3

∴ n = 31/3 + 1

= 34/3

= 11 1/3

Since, n should be positive integer.

So, 0 is not a term of the given AP.

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 5 Arithematic Progressions
Exercise 5.2 | Q 5 | Page 49
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