Question 46

The sum of 18 consecutive natural numbers is a perfect square. The smallest possible value of this sum is

Name: The sum of 18 consecutive natural numbers is a perfect square. The smallest possible value of this sum is
Uploaded: 2026-06-19T17:25:03.992048+05:30
Duration: 6 min 25 s
Description: The sum of 18 consecutive natural numbers is a perfect square. The smallest possible value of this sum is

Solution

Let 18 consecutive natural number = a, a + 1, a + 2, a + 3, ........., a + 17.

Sum = $$\frac{n}{2}[2a + (n - 1)d]$$

= $$\frac{18}{2}[2a + (18 - 1)1]$$

= 9 (2a + 17)

= 18a + 153

Put a = 1, Sum = 18 + 153 = 171

Put a = 2, Sum = 36 + 153 = 189

Put a = 3, Sum =54 + 153 = 207

Put a = 4, Sum =72 + 153 = 225 [Required answer]

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