Statement A (Assertion): a, b, c are in AP if and only if 2b = a + c. Statement B (Reason): The sum of first n odd natural numbers is n². e. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion(A). f. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). g. Assertion (A) is true but reason (R) is false. h. Assertion (A) is false but reason (R) is true.
Question
Statement A (Assertion): a, b, c are in AP if and only if 2b = a + c. Statement B (Reason): The sum of first n odd natural numbers is n². e. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion(A). f. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A). g. Assertion (A) is true but reason (R) is false. h. Assertion (A) is false but reason (R) is true.
Solution
The correct answer is f. Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
Explanation: Statement A is a definition of an arithmetic progression (AP). In an AP, the difference between any two consecutive terms is constant. If a, b, and c are in AP, then the difference between b and a should be equal to the difference between c and b. This gives us 2b = a + c.
Statement B is also true. The sum of the first n odd natural numbers is indeed n². This can be proven by induction or by directly adding the numbers.
However, statement B does not explain or is not related to statement A. They are two separate mathematical facts. Therefore, while both statements are true, the reason (R) is not the correct explanation of the assertion (A).
Similar Questions
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