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

Solution:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.

Let 0 be the nth term of given AP, (aₙ = 0)

From the question given,

a = 31,

d = 28 - 31 = - 3

The nth terms of an AP, is

aₙ = a + (n - 1 )d.

Substituting the values, we get,

0 = 31 + (n - 1)(-3)

3(n - 1) = 31.

Dividing both sides by 3, we get,

n - 1 = 31/3.

n = 31/3+ 1

n = 34/3.

As, n should be a positive integer, 0 is not a term given in the AP.

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

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☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.2 Problem 5

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

Summary:

An arithmetic progression is a sequence where each term, except the first term, is obtained by adding a fixed number to its previous term. 0 is not a term of the AP: 31, 28, 25, …

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