1973-12-13 — Page 19

GITY

育教備舖頁三第張五第日九十月一十年丑発展發

橋

1974中學會考試題預習專欄

與世書院L

數學科(薢程乙)(六) 文長波

Mathematica (6)

報日僑

四期星

日三十月二十年三七九一艇公年二十六國民華中

Solution: eta be the first term of the series, r be the common rutio of the

constant

is also a constant

*(x+y)=(a:constant)(x2+y? y

(+)?

Geometric Propression

"A reometric progression is a Series in which any term after the

firat is obtained by multiplying

the one before. it by a constant. quantity. Formulas:

T(n)=arl-

2. S(n)_a(r”—1)

Let C be the cost in $,

N be the number of goods, then CakykN

kN where:kysky are constants..

sries.

T(2)=ar-

(5)=er4

Sum to infinity="_

when r=20

The general

(2)

the first term in the n

bracket= n(n-1)+11.

-n-n+t

ation: the first term in the 2nd

bricket=3=2x1+1

The first term' in the 3rd bracket=73x2+1.

The first term in the 4thi brackete13#4x3+1

Solution to exercise 5 2b+2c-2a

2c+2a-2b

where T(n)=n

3740=kg + 80kg 7100=k, +200k2

(2)

(2)−(1)→120k2=3360

C-1500+28N

Add the ninerators and dino-

minutors of each Swo ratios.

when y = 400,C

The cost is $12700,

(2b+2c-

2c)+(2a+2b-2c),

雞雞

)+(2b+2c−2a)

constant.

>(y-x)(x-y)=kccy

where k

1500+28x400 12700

Arithishic Pro Tession

An arithmetic progression is

a series in which successive terms 'increase or decrease by a cominori

difference.

Formulas; 11(n)=a+(n-1)d

$(n)=(a+1)

-[2-(n-1)α)

T(n) term (1.e.gen

term)

d- Common difference.

fiATI:

5(n)=Sum of first n

n-number of terms

term (ice.genera ...term)

ri = Common. rutia

n=number of terms

a 1st term

S(n)- Sum of first 'n tera

When 3 quantities are in. geometricnro_ression. The middle one is said to be the geometric. mean of the other thos

Fxample

fu,b,c are in G.P then b-jac

The sum of 3. numbers in A.P. is 27 and the sum

of their square is 293. Find them

Solution: Let be the middle.

number, be the common; difference.

The 3 numbers, ure a-d, a and a+d respectively. (a−d)+a+(c+d)=27 (1) (a+d)+a*+ (a+a)=293-

from(1) 3a=27.

2

a=9

(2)

Subst.ang into (?)(9+a)/+9?

+(9rd) =293 81-18d+d2 .481+814

18d+d2 3 2d=500

Example

Express 0.45 in the form of a common friction,

Solution: 0.45-0.454545.

=0.45+0:0045+0.00045

0.45 1−0.

xample

Prove that the sum of the terms within the a bracket of the Series.. ( 1 ) + ( 3+5)+(7+9+11) + (13+ 15+17+19) +

is n and that the sun- of the terms in the fin n brickets' is ne(n+1

= # [2(n2-1+1)+(n=1)x2]

(Sus of terms in the first

n brackets

3(n+1) (2 + (2 (n+1)-1 ] x2}

Exercise

The 7 term of a A.P. is 44 ana: the sum of the first: 10 terms is 330. Pind the first. term of the progression, the Common difference: aid the sum of the first 18 terms,

2. The middle points of the sides

of a triangle are joined, forming a second triangle, a third triangle.ic formed by joining the middle points of the second, and the process is continued indifinitely. If the pirimeter and area of the original triang le are 10 cm and 30 sq. cm respectively find:a) the sum of

the peri- meter.

x+y=(

also x

x+y)=(4−ki)xy

-(2)

when.3 quantities are in

arithmetic progression, the middle. one is said to be the arithmetic

Examle

mean of the other two. The arithme- tic mean of a and b is (a+b).

5th term

出日華 版報僑

律香

吾德門

片救智業彩

映献天今

The 14.

numbers ar

and

Find. the general term of the geometric progress

ions with 2nd term

4.

number of terms.in the:

or ckets=1+2+3+..

号(n+1)

the 1st Üracket neg

1 term; 2nd bricket

院戲大年萬

冷藏毓、慈能力,

TEL:264402

The gut of

the area of

ull, the triangleg,

3.Find: the sum of all even number's

from 14 to 200 inclusive,

excluding. Prose which are

multiples of 5.

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