Two distinct terms of an A.P. cannot be...... | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) An Arithmetic Progression $(A.P.)$ is defined as a sequence of numbers such that the difference between any two consecutive terms is constant,know

Vedclass · Accepted Answer

equal

Vedclass · Answer

(D) An Arithmetic Progression $(A.P.)$ is defined as a sequence of numbers such that the difference between any two consecutive terms is constant,known as the common difference $(d)$.If an $A.P.$ has a common difference $d 
eq 0$,then every term in the sequence is distinct.If two terms of an $A.P.$ were equal,say $a_n = a_m$ for $n 
eq m$,then $a + (n-1)d = a + (m-1)d$.This simplifies to $(n-1)d = (m-1)d$,which implies $(n-m)d = 0$.Since $n 
eq m$,we must have $d = 0$.However,the question specifies 'distinct terms' of an $A.P.$,which implies the terms must be different from each other.Therefore,two distinct terms of an $A.P.$ cannot be equal.

Two distinct terms of an $A.P.$ cannot be........

Similar Questions

The difference between two consecutive terms of an $A.P.$ is denoted by.........

Which of the following sequences is an $A.P.$?

Find the sum of the first $25$ terms of the $A.P.$ $3, \frac{9}{2}, 6, \frac{15}{2}, \ldots$

If $a=2$ and $d=4,$ then $S_{40}=\ldots \ldots \ldots$

How many numbers lie between $10$ and $300,$ which when divided by $4$ leave a remainder $3?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module