Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 46
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]
