Question

the sum of 18 consecutive natural number is a perfect square the smallest possible value of this sum is​

Answer 1

Solution:

Let the number be

a, a + 1, a + 2, a + 3 _ _ _ _ _ _ a + 17.

This is an AP.

First term = a

Common difference, d = 1

Terms, n = 18

Sum of the terms

Substitute the values :

Sn = n/2 [ 2a + (n - 1)d ]

=> Sn = 18/2 [ 2a + 17 ]

=> Sn = 9 [ 2a + 17 ]

=> Sn = 18a + 153

For a = 1, Sn = 171

a = 2, Sn = 189

a = 3, Sn = 207

a = 4, Sn = 225

Here, 225 is the perfect square of 15.

Thus, 15 is a perfect square the smallest possible value of this sum is 225.

Answer 2

Answer:

225...................................................................