The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the 15th group is equal to

The pattern of the groups is such that the first group has 1 number, the second group has 3 numbers, the third group has 5 numbers, and so on. This is an arithmetic sequence where the common difference is 2.

The nth term of an arithmetic sequence can be found using the formula: a + (n - 1)d, where a is the first term, d is the common difference, and n is the term number.

In this case, a = 1 (the first term), d = 2 (the common difference), and n = 15 (the group number we're interested in).

So, the number of terms in the 15th group is: 1 + (15 - 1) * 2 = 29.

The numbers in the 15th group are the 29 natural numbers starting from the sum of the numbers in the first 14 groups plus one.

The sum of an arithmetic series can be found using the formula: n/2 * (a + l), where n is the number of terms, a is the first term, and l is the last term.

The sum of the first 14 groups is: 1/2 * 14 * (1 + 27) = 196.

So, the first number in the 15th group is 196 + 1 = 197.

The last number in the 15th group is 197 + 29 - 1 = 225.

So, the sum of the numbers in the 15th group is: 29/2 * (197 + 225) = 6131.