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1, 3, 5, 7, 9, … + 2 TermNumbersPattern 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

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2, 4, 6, 8, 10, … + 2 TermNumbersPattern 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

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1 x2 2 x 3 3 x 4 2612 … … x … … TermNumbersPattern of Numbers n th term = n 2 + n 1 2 3 … n 2 6 12 … ? 1 ( 1 + 1) = 2 … 2 ( 2 + 1) = 6 3 ( 3 + 1) = 12 n ( n + 1) = n 2 + n

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13610 15 … … TermNumbersPattern of Numbers 1 2 3 … n 1 3 6 … ? …

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1 x1 2 x 2 3 x 3 4 x 4 5 x 5 … … … 1 4 9 16 25 n th term = n 2 TermNumbersPattern of Numbers 1 2 3 … n 1 4 9 … ? (1) 2 = 1 (2) 2 = 4 (3) 2 = 9 (n) 2 = n 2 …

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TermNumbersPattern of Numbers 1 1 1 1 2 1 1 3 3 1 14 6 4 1 1 2 4 8 16 1 2 3 … n 1 = 2 0 … ? 2 = 2 1 4 = 2 2 2 1 – 1 2 2– 1 2 3 – 1 2 n – 1 … n th term = 2 n – 1

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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 = n 2 = 10 2 = 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 term Therefore, 1 + 3 + 5 + 7 + 9 + 11 = n 2 = 6 2 = 36 6 term

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2. Find the line of the pattern of Pascal Triangle numbers if the sum of the lines is 256! Solution 256 = 2 n – 1 2 8 = 2 n – 1 8 = n – 1 n = 8 + 1 n = 9 Hence, the pattern of Pascal Triangle numbers where the sum is 256 is the 9 th lines 3. Find the pattern of rectangle numbers until the 9 th term! Solution TermPattern 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

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1.Find the next three figures from the following figures! 2.Find a.The 20 th order of the pattern of square numbers; b.The 28 th order of the pattern of square numbers; c.The 30 th order of the pattern of square numbers! 3.Copy the figure of Pascal Triangle and then continue until the 10 th line! 4.Find the sum of following Pascal Triangle numbers lines a. The 8 th lines; b.The 10 th lines! 5. Find how many terms of the first even numbers, if the sum is 156!

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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 n th term = n 2 n th term = 2 n – 1 3. Pattern of rectangle numbers n th term = n 2 + n

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