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

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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

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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........

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