3. These lengths give a pattern 1, 2, 3, 4, ..., 10,
which is an AP with first term 1 and common difference 1.
4. Sum of first ten terms
= 1 + 2 + 3 + ... +10 = 55
(1)
Area of the shaded region
(area of rectangle ABCD)
==x10x11, which is same as obtained in (1) above. This shows that the
sum of the first 10 natural numbers is
This can be generalised to find the sum of first n
atural numbers as
5.- (+1)
(2)
NCS
e repub TV
OBSERVATION
For n = 4,S.
For n = 12, S. =
For n = 50, S =
For n = 100, S.
Conclusion