Statement 1: The numbers  cannot be the terms of a single A.P. with non-zero common difference Statement 2: If  are terms (not necessarily consecutive) of an A.P., then there exists a rational number  such that   a)  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1 b)  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1 c)  Statement 1 is True, Statement 2 is False d) Statement 1 is False, Statement 2 is True

Question ID - 51113 | Toppr Answer Statement 1: The numbers  cannot be the terms of a single A.P. with non-zero common difference Statement 2: If  are terms (not necessarily consecutive) of an A.P., then there exists a rational number  such that   a)  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1 b)  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1 c)  Statement 1 is True, Statement 2 is False d) Statement 1 is False, Statement 2 is True

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Answer Key : (a) -

(a)

Let  be the  and  terms of an A.P. Then

and

Hence,   and , so that

Since,  are positive integers and  is a rational number. From (1), using , we have

Hence,  cannot be the terms of an A.P.