1, 3, 5, 7, 9, … + 2 termnumberspattern of numbers the n-order for the pattern of odd numbers is...
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1 , 3 , 5 , 7 , 9 , …+ 2
+ 2
+ 2
+ 2Term Numbers Pattern of
Numbers
The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers
1
2
3
4
n
1
3
5
7
?
2 (1) – 1 = 1 2 (2) – 1 = 3
2 (3) – 1 = 5
2 (4) – 1 = 7
2 (n) – 1 = 2n – 1
2 , 4 , 6 , 8 , 10 , …+
2+ 2
+ 2
+ 2Term Numbers Pattern of
Numbers
The n-order for the pattern of even numbers is 2n, for n is natural numbers
1
2
3
4
n
2
4
6
8
?
2 (1) = 2 2 (2) = 4
2 (3) = 6
2 (4) = 8
2 (n) = 2n
1 x2
2 x 3 3 x 4
2 6 12 …
… x …
…
Term Numbers Pattern of Numbers
nth term = n2 + n
1
23
…
n
2
612
…
?
1 ( 1 + 1) = 2
…
2 ( 2 + 1) = 6
3 ( 3 + 1) = 12
n ( n + 1) = n2 + n
1 3 6 10 15 …
…
Term Numbers Pattern of Numbers 1 1 1 2
12 2
2 2 1 63
2 2
3 3 1 126
2 2
12
n n
1
2
3
…
n
1
3
6
…
?
…
1 x1
2 x 2
3 x 3
4 x 4
5 x 5 …
…
…
1 4 9 16 25
nth term = n2
Term Numbers Pattern of Numbers 1
23
…
n
1
49
…
?
(1)2 = 1(2)2 = 4(3)2 = 9
(n)2 = n2
…
Term Numbers Pattern of Numbers
11 1
1 2 11 3 3 1
1 4 6 4 1
1248
16
1
23
…
n
1 = 20
…
?
2 = 21
4 = 22
21 – 1
22– 1
23 – 1
2n – 1
…
nth term = 2n – 1
1. Find the sum of a. 1 + 3 + 5 + 7 + 9 + 11!b. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 !
Solution
The pattern of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 is the first of 10 0dd numbers, so n = 10.
10 term
Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = n2 =
102 = 100
10 term
b.
a. The pattern of 1 + 3 + 5 + 7 + 9 + 11 is the first of 6 0dd numbers, so n =
6.6 termTherefor
e,1 + 3 + 5 + 7 + 9 + 11 = n2 = 62 = 36
6 term
2. Find the line of the pattern of Pascal Triangle numbers if the sum of the lines is 256!Solution
256 = 2n – 1
28 = 2n – 1
8 = n – 1 n = 8 + 1 n = 9
Hence, the pattern of Pascal Triangle numbers where the sum is 256 is the 9th lines
3. Find the pattern of rectangle numbers until the 9th term!Solution Term Pattern of
NumbersNumbers
1 1 ( 1 + 1) 2
2 2 ( 2 + 1) 6
3 3 ( 3 + 1) 12
4 ... …
5 … …
6 … …
7 … …
8 … …
9 … …
2, 6, 12, 20, 30, 42, 56, 72, 90
1. Find the next three figures from the following figures!
2. Find a. The 20th order of the pattern of square numbers;b. The 28th order of the pattern of square numbers;c. The 30th order of the pattern of square numbers!
3. Copy the figure of Pascal Triangle and then continue until the 10th line!
4. Find the sum of following Pascal Triangle numbers linesa. The 8th lines;b. The 10th lines!
5. Find how many terms of the first even numbers, if the sum is 156!
1. Pattern of odd numbers
The n-order for the pattern of odd numbers is 2n – 1, for n is natural numbers
2. Pattern of even numbers
The n-order for the pattern of even numbers is 2n, for n is natural numbers
4. Pattern of triangle numbers
5. Pattern of square numbers
6. Pattern of Pascal triangle numbers
12
n n
nth term = n2
nth term = 2n – 1
3. Pattern of rectangle numbers
nth term = n2 + n