Even numbers from 2 to 50: 2, 4, 6, ..., 50.

This is an AP with first term = 2, last term = 50, common difference = 2.

Number of terms = 25.

Sum = 25(2+50)/2 = 25 × 26 = 650

Let original number = x.

Then x + 25% of x = 500.

So x + 0.25x = 500, 1.25x = 500, x = 400

Let smaller number = x, larger = 2x.

Then 2x - x = 45, so x = 45.

Numbers are 45 and 90.

Let integers be n-1, n, n+1.

Sum = 3n = 81, so n = 27.

The three integers are 26, 27, 28.

Largest = 28

Sum of squares = 1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55.

Formula: n(n+1)(2n+1)/6 = 5×6×11/6 = 55

LCM(9, 11) = 99 (since 9 and 11 are coprime).

Smallest three-digit multiple of 99 is 99 × 2 = 198.

20 = 2² × 5.

Sum of divisors = (1 + 2 + 4)(1 + 5) = 7 × 6 = 42.

Divisors are: 1, 2, 4, 5, 10, 20.

32 ÷ 7 = 4 remainder 4 (No). 33 ÷ 7 = 4 remainder 5 (No). 34 ÷ 7 = 4 remainder 6 (No). 32 = 7×4 + 5 = 28 + 5 (Yes). 32 ÷ 7 gives remainder 5.

Digital root = 9 + 8 + 7 + 6 = 30 → 3 + 0 = 3.

Alternatively, since the sum is divisible by 9, the digital root is 9.

Wait: 9+8+7+6 = 30, 3+0 = 3.

So digital root is 3.

Using HCF × LCM = Product of two numbers: 15 × 180 = 45 × x.

Therefore, 2700 = 45x, so x = 60.