Question

Question 5
Is 0 a term of the AP 31, 28, 25, …? Justify your answer.

Answer 1

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

Given that, first term a = 31,
Common difference, d = 28 – 31 = - 3

The nth terms of an AP is given by,
$a_n=a+(n-1)d$
$\Rightarrow 0=31+(n-1)(-3)$
$\Rightarrow 3(n-1)=31$
$\Rightarrow n-1=\frac{31}{3}$
$\therefore n=\frac{31}{3}+1=\frac{34}{3}=11\frac{1}{3}$
Since n is not a positive integer, 0 is not a term of the given AP.