Question

Assertion (A): The mean of the first ten natural numbers is 5.5.

Reason (R): The sum of the first ten natural numbers is $$\frac{n(n + 1)}{2}$$.

विकल्प

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The sum of the first ten natural numbers is 55, so their mean is $$\frac{55}{10} = 5.5$$.

Step 2 – Reason: R is true. The sum of the first $$n$$ natural numbers is $$\frac{n(n + 1)}{2}$$.

Step 3 – Link: Using the formula in R with $$n = 10$$ gives the sum 55, which establishes the mean stated in A.