CAT 2021 Slot 1 QA Question 5: 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

Question

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

Accepted Answer

The group sizes are 1, 3, 5, and so on. Hence, the 15th group has 29 numbers.
The total number of terms before the 15th group is the sum of the first 14 odd numbers.
$1 + 3 + 5 + \ldots + 27 = 14^2 = 196$
So the 15th group starts at 197 and ends at 225.
The required sum is
$\dfrac{29}{2}(197+225) =