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 |
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 |
(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.