Statement A (Assertion): -5,2,0,5 is an Arithmetic Progression. Statement B (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers. a. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion(A). b. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). c. Assertion (A) is true but reason (R) is false. d. Assertion (A) is false but reason (R) is true.
Question
Statement A (Assertion): -5,2,0,5 is an Arithmetic Progression. Statement B (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers. a. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion(A). b. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). c. Assertion (A) is true but reason (R) is false. d. Assertion (A) is false but reason (R) is true.
Solution
c. Assertion (A) is true but reason (R) is false.
Explanation: Statement A is true because -5, 2, 0, 5 is indeed an Arithmetic Progression (AP). An AP is a sequence of numbers in which the difference of any two successive members is a constant. Here, the common difference is 5-0=2-(-5)=5, which is a constant.
Statement B is false because the terms of an Arithmetic Progression can have both positive and negative rational numbers. There is no such rule that an AP cannot have both positive and negative numbers. The only requirement for a sequence to be an AP is that the difference between successive terms should be constant.
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