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Grade 12th passAlgebra

The series of natural numbers is divided into groups as follows; (1), (2, 3), (4, 5, 6,), (7, 8, 9, 10) and so on. Find the sum of the numbers is the nth groups is ?
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Profile image of ayush singhal
7 Years agoGrade 12th pass
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1 Answer

Profile image of Aditya Gupta
7 Years ago
in the nth group, the last number will be n(n+1)/2 [by observation that last numbers 1, 3, 6, 10,.... are actually the sum of first n numbers, which is equal to n(n+1)/2]
now, number of terms in nth group is obviously n
so by sum of an AP, taking first term as the last term, difference as – 1, and number of terms n, we have
Sn= n/2*[2*n(n+1)/2+(n – 1)*( – 1)]
=n*(n^2+1)/2

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