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

Do $1, 1, 1, 2, 2, 2, 3, 3, 3, \ldots$ form an $AP$? If they form an $AP$,write the next two terms.

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

For the $AP: \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots,$ write the first term $a$ and the common difference $d$.

The first four terms of an $AP,$ whose first term is $-2$ and the common difference is $-2,$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module