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
Explanation:
Here, 1st group has 1 integer 2nd group has 3 integers 3rd group has 5 integers ∴ nth groups will have (2n – 1) integers.
Total inters used till 1st group = 1 = 12 2nd group = 1 + 3 = 22 3rd group = 1 + 3 + 5 = 9 = 32
∴ Total integers used till nth group = n2
∴ Sum of integers in 15th group = Sum of all integers used till 15th group - Sum of all integers used till14th group
= (1 + 2 + 3 + … + 152) - (1 + 2 + 3 + … + 142)
= 225×2262 - 196×1972
= 25425 – 19306 = 6119
Hence, option (b).
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