Kamis, 27 Januari 2011
To : Agnes and friends 9 ( PIS )
Arithmetic Sequences
Arithmetic formula: Un = U1 + (n - 1)b
middle term : (Un + U1):2
find number of terms n = ((Un-U1):b)+ 1
Sample problems:
Find the first four terms of this arithmetic sequence.
1) Un = 3n + 2 To find the first four terms, in a row, replace n with 1, then 2, then 3 and 4
Answer: 5, 8, 11, 14 The sequence is arithmetic! b = 3
Find a formula for each sequence.
1) 2, 5, 8, 11, 14, . . .
Work: It is arithmetic! So use the arithmetic formula you learned above!
U1 = 2, look at the first number in the sequence!
d = 3, look at the common difference!
Therefore, Un = 2 + (n - 1)3 and simplifying yields : Un = 3n -1 ( tada!)
Try putting in 1, then 2, then 3, etc. and you will get the sequence!
Find the indicated term of the sequence.
1) sequence is arithmetic with U1 = 5 and U7 = 29. Find U53
Work: Use the formula! 29 = 5 + 6d Where oh where did I get that! Substitution!
24 = 6d means d = 4
U53 = 5 + 52.4 = 213
2) Find the number of multiples of 9 between 30 and 901.
Work: What's the first multiple of 9 in the range? How about 36.
What's the last multiple of 9 in the range? How about 900.
Use the formula: 900 = 36 + 9(n - 1) and solve for n!
864 = 9n - 9
873 = 9n
97 = n There are 97 multiples in the range!
The next problems :
How to find the different of arithmatic sequence ,If we want insert 4 number between 10 and 50 .
works : difference (d) = (50 - 10 ): (4 + 1) = 8
so the sequences are : 10 , 18 , 26 , 34 , 42 , 50
Arithmetic Series
Sn=(2a+(n-1)b)n/2 ,Sn= sum of n terms
sample problems:
Find the sum of the given arithmetic series:
6 + 12 + 18 + 24 + ...72
U1=6 , b=6 find n = ((Un-U1):b)+ 1 = ((72-6):6)+ 1 =11 + 1= 12
Un=72 Now find S12 = (2.6+(12-1)6) 12/2 = 468
Geometric sequence
Geometric formula: Un = U1 . r^(n - 1) ,^= r pangkat (n-1)
Example:
4, 8, 16, 32, . . .
Work: It is geometric! So use the geometric formula you learned up yonder!
t1 = 4, look at the first number in the sequence!
r = 2, look at the common ratio!
Therefore, Un = 4 . 2^(n - 1) and simplifying gives us: Un = 2.2^n (Yikes stripes! Where did this come from. rewrite 2^(n - 1) as 2^n . 2^-1 and cancel with the four!)
Geometric Series
So, the sum of n terms of a geometric series with starting value a, ratio, r is:
Sn = U1(1-r^n)/1-r
middle tewrms :akar dari U1.Un
PRACTICE ,PRACTICE AND PRACTICE ! FOR MORE PRACTICE, SEE THIS SITE: http://hotmath.com/help/gt/genericalg2/section_9_2.html
Arithmetic formula: Un = U1 + (n - 1)b
middle term : (Un + U1):2
find number of terms n = ((Un-U1):b)+ 1
Sample problems:
Find the first four terms of this arithmetic sequence.
1) Un = 3n + 2 To find the first four terms, in a row, replace n with 1, then 2, then 3 and 4
Answer: 5, 8, 11, 14 The sequence is arithmetic! b = 3
Find a formula for each sequence.
1) 2, 5, 8, 11, 14, . . .
Work: It is arithmetic! So use the arithmetic formula you learned above!
U1 = 2, look at the first number in the sequence!
d = 3, look at the common difference!
Therefore, Un = 2 + (n - 1)3 and simplifying yields : Un = 3n -1 ( tada!)
Try putting in 1, then 2, then 3, etc. and you will get the sequence!
Find the indicated term of the sequence.
1) sequence is arithmetic with U1 = 5 and U7 = 29. Find U53
Work: Use the formula! 29 = 5 + 6d Where oh where did I get that! Substitution!
24 = 6d means d = 4
U53 = 5 + 52.4 = 213
2) Find the number of multiples of 9 between 30 and 901.
Work: What's the first multiple of 9 in the range? How about 36.
What's the last multiple of 9 in the range? How about 900.
Use the formula: 900 = 36 + 9(n - 1) and solve for n!
864 = 9n - 9
873 = 9n
97 = n There are 97 multiples in the range!
The next problems :
How to find the different of arithmatic sequence ,If we want insert 4 number between 10 and 50 .
works : difference (d) = (50 - 10 ): (4 + 1) = 8
so the sequences are : 10 , 18 , 26 , 34 , 42 , 50
Arithmetic Series
Sn=(2a+(n-1)b)n/2 ,Sn= sum of n terms
sample problems:
Find the sum of the given arithmetic series:
6 + 12 + 18 + 24 + ...72
U1=6 , b=6 find n = ((Un-U1):b)+ 1 = ((72-6):6)+ 1 =11 + 1= 12
Un=72 Now find S12 = (2.6+(12-1)6) 12/2 = 468
Geometric sequence
Geometric formula: Un = U1 . r^(n - 1) ,^= r pangkat (n-1)
Example:
4, 8, 16, 32, . . .
Work: It is geometric! So use the geometric formula you learned up yonder!
t1 = 4, look at the first number in the sequence!
r = 2, look at the common ratio!
Therefore, Un = 4 . 2^(n - 1) and simplifying gives us: Un = 2.2^n (Yikes stripes! Where did this come from. rewrite 2^(n - 1) as 2^n . 2^-1 and cancel with the four!)
Geometric Series
So, the sum of n terms of a geometric series with starting value a, ratio, r is:
Sn = U1(1-r^n)/1-r
middle tewrms :akar dari U1.Un
PRACTICE ,PRACTICE AND PRACTICE ! FOR MORE PRACTICE, SEE THIS SITE: http://hotmath.com/help/gt/genericalg2/section_9_2.html
Selasa, 25 Januari 2011
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