S'6 math

1(a) Consider the following sequence:

a1 = 1
a2= 1+2(1) = 3
a3= 1 + 2(1) + 2(2) =7
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a(n) =1+ 2(1) + 2(2) + ‧‧‧+ L

(i) Write down the values of a4 and a5. 我知道這條點做。
a4 = 1 + 2(1) + 2(2) + 2(3) = 13
a5 = 1 + 2(1) + 2(2) + 2(3) + 2(4) = 21


可否列式
(ii) Express the last term L of a(n) in terms of n, and hence simplify the
expression of a(n). Ans: L = 2 (n-1), a(n) = 1+ n(n-1)

(b) Consider the following sequence:

b1﹕1
b2﹕3, 5
b3﹕7, 9, 11
b4﹕ 13, 15,17,19
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b(n) ﹕a(n), a(n)+2, a(n)+4, ‧‧‧, L

(i) Express the last term L of b(n) in terns of n. Ans:L=n(n+1) -1=1

(ii) Using the result obtained in(a), or otherwise, find the sum of the terms in b(n).
Ans:n^3

2. An auditorium has 50 rows of seats. All seats are numbered in numerical
order from the first row to the last row, and from left to right, as shown in the
figure. The first row has 20 seats. The second row has 22 seat. Each
succeeding row has 2 more seats than the previous one.

The figure of the seats:

：
：

3rd row [ 43 | 44 | ‧‧‧‧‧‧65 | 66 ]
2nd row [ 21 | 22 |‧‧‧‧‧‧41 | 42 ]
1st row [ 1 | 2 |‧‧‧‧‧‧‧19 | 20 ]

(a) How many seats are there in the last row? 我知道這條點做。
a=20, d=2
T(50) = 20+ (50 -1)(2) = 118 seats

(b) Find the total number of seats inthe first n rows. 我知道 this ans is 19n+n^2

但是, 我不懂這條：
Hence determine in which row the seat numbered 2000 is located.

回答其中一條就可以。謝謝!