Question

Consider the following:

Assertion (A): \(1^2 + 3^2 + 5^2 + \cdots + 39^2 = 10760\)

Reason (R): The sum of the squares of the first \(n\) odd numbers is \[ \frac{n(4n^2-1)}{3}. \]

The correct answer is:

• A. Both A and R are correct and R is the correct explanation of A
• B. Both A and R are correct and R is not correct explanation of A
• C. A is correct, but R is not correct
• D. A is incorrect, but R is correct

Hint:

To quickly sum squares of odd numbers up to a last term \( L \), use the alternative formula \( \frac{n(L)(L+2)}{3} \) where \( n \) is the number of terms and \( L \) is the last odd number. Here, \( \frac{20 \times 39 \times 41}{3} = 10660 \).

Answer 1

The Correct Option is D