deret matika

A. Line
Number lines are number gathering with level given arrangement and formed terminological one given order. Numbers of line were called by tribe.

B. Line Accounts
Line accounts is number line that each number it after tribe first got by adds number in advance with one the so called constant number difference.
Example: 3, 7, 11, 15, …
Example upon constitutes one line account because each its tribe got by adds 4 to previous numbers. In line accounts 50, 45, 40, … difference = 45 50 = 5

Line formula accounts
1. Tribe goes to n or tribal last:


2. Total n first tribe:

Prove:
or
………. Equation 1
This equation gets too be written as follows:
………. Equation 2
With add equation 1 and equation 2 we will get:




n tribe


Because of, therefore Sn can also be declared for as follows.

Formula foots up n first line tribe aritmatika is
or
With Sn = jummlah n tribe
n = a lot of tribes
a = first tribe
b = differences
Un = tribe goes to n
Example:
Known one line accounts 3, 7, 11, … with a = 3, b = 7 – 3 = 4,
Total 6 first triare:


C. Geometry line
Geometry line is number line that each its number is gotten with multiply number in advance with konstanta ratio the so called.
Example:
a. 5, 10, 20, 40, …
Example upon constitute geometry line that setipa its number is gotten with multiply number in advance with 2.
b. 9, -3, 1,
Its ratio is

Formula for geometry line
1. Tribe goes to n or tribal last


2. Total n first tribe

Prove:
or

By multiplies both of equation internode 1 by r, gotten by equation 2 followings

Now kurangkan equation 2 by equations 1.



With Sn = jummlah n tribe
n = a lot of tribes
a = first tribe
r = ratios
Un = tribe goes to n
Example:
Known one geometry line 5, 10, 20, …a = 5, r = 2, .
Total seven first tribe = = 635
D. Line Geometry not Until
Line geometry not until is geometry line with many its tribal not get until by.
Formula for totals geometry line tribe not until be
with
Since therefore 1< r< 1 so acquired rn wends 0
Accordingly
Example:
Known by line geometry not until with a = 1, r =.
Total a lot of tribes until not until are

E. Harmonious line
Harmonious line is number line that inversely forms one line account.
Example:
are one harmonious line because is one line account.

F. Averagely
Terms among two tribe that give to be called average among two that tribe.
In geometry line 2,-4, 8, -16, … two geometry average among 2 and 16 are 4 and 8.
In harmonious line average among and is


Training

A. Line Accounts
1. Look for 40th tribe and total 40 first tribe of computing line 10, 8, 6, …
2. Computing foots up 100 first positive integers that depleted being divided 7
3. One line accounts to have first tribe 4 and tribal last 34. If its terms amount 247 look for a lot of tribes and its difference!
4. Look for three line deep numbers account in such a way face so first triamount and third be 12 and yielding first tribal times and second be 24!
5. Look for three line deep numbers account that amount the 48 and total its squares 800!
6. Three number form compares 2:5:7. If 7 dikurangkan of second number therefore its number forms one line account. Numbers drd determinative originally!
7. One place glides with rolled out zoom built upon by rolled out surface and having 10 penyanggah's pillars that its distance with one by another. penyanggah high the very top is do splits and most short 2 foots. Tall determinative each penyanggah that needful!
8. Determinative average accounts among and!
9. Interpolate 4 average account among 9 and 24!

B. Geometry line
1. Look for 8th tribe and total 8 first tribe of lines 4, 8, 16, …
Second tribe of one line geomatri is 3 and tribal to five the be, look for tribe eight!
2. Look for three number who can form geometry line by totals 26 and perkaliannyaadalah 216!
3. Two first tribe of geometry lines are and. Point out that amount n tribe of this line gave by formula
4. Look for total n first tribe of geometry lines
5. Interpolate two geometry average among 3 and 192!
6. Averagely geometry of two number are 8. If one of number it is 6 look for lainnnya's numbers!

C. Line Geometry not Until
1. Look for total line geometry not until following!

2. Declare for each decimal following as one fraction!
a. 0,444 …
b. 0,4272727 …
3. Total two first tribe of menurun's geometry line is and amounts until not until be. Write three first tribe of that geometry line!

D. Harmonious line
1. Account 15th tribe of harmonious line
2. Determinative average harmonious among and!
3. Interpolate four harmonious averages among and!
4. Interpolate four harmonious averages among and!