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11. Arithmetic Progression
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Q17 of 178 Page 548

Find the sum of first n natural numbers.

First n natural numbers are 1, 2, 3,…, n.

To find: sum of these n natural numbers.


The natural numbers forms an AP with first term 1 and common difference 1.


Now, Sum of first n terms of an AP is given by:


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


where a is the first term and d is the common difference.


∴ Sum of first n natural numbers is given by:


Sn = [2(1) + (n - 1)(1)]


= [2 + n - 1]


= [n + 1]


∴ Sum of first n natural numbers is n(n + 1)/2.


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Questions · 178
11. Arithmetic Progression
1 1 1 1 1 2 2 2 2 2 3 4 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 1 1 1 1 2 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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