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
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OBSERVATION
For n = 4,S.
For n = 12, S. =
For n = 50, S =
For n = 100, S.
Conclusion

The rumpart family is building a new room onto their house. the width of the new room will be 16 feet. the length of the room will be 4% greater than the width. write an expression to find the length of the new room. what will be the area of this new room?

Aportion of a hiking trail slopes downward at about an 84° angle. to the nearest tenth of a flot, what is the value of x, the distance the hiker traveled along the path, if he has traveled a horizontal distance of 120 feet? a. 143.3 b. 12.5 c. 120.7 d. 130.2

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?