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

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Let $0$ be the $n^{th}$ term of the given $AP$,i.e.,$a_n = 0$.
Given that,the first term $a = 31$ and the common difference $d = 28 - 31 = -3$.
The $n^{th}$ term of an $AP$ is given by the formula:
$a_n = a + (n - 1)d$
Substituting the values:
$0 = 31 + (n - 1)(-3)$
Rearranging the terms:
$3(n - 1) = 31$
$n - 1 = \frac{31}{3}$
$n = \frac{31}{3} + 1 = \frac{34}{3} = 11 \frac{1}{3}$
Since $n$ must be a positive integer (representing the position of a term),and $11 \frac{1}{3}$ is not an integer,$0$ is not a term of the given $AP$.

Explore More

Similar Questions

The ratio of the $11^{\text{th}}$ term to the $18^{\text{th}}$ term of an $AP$ is $2:3$. Find the ratio of the $5^{\text{th}}$ term to the $21^{\text{st}}$ term,and also the ratio of the sum of the first five terms to the sum of the first $21$ terms.

Difficult
View Solution

The sum of the first five multiples of $3$ is

For the $A.P.$ $3, 8, 13, 18, \ldots$,$T_{n} = \ldots$

Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.

The $21^{\text{st}}$ term of the $AP$ whose first two terms are $-3$ and $4$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo