Adding a Sequence of numbers (Pairing Method)

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Presentation transcript:

Adding a Sequence of numbers (Pairing Method) 1. Find the sum of 1 + 2 + 3 ……. + 49 + 50 Problem Solving Strategy :- Step 1 – Divide the last number by 2 50 ÷ 2 = 25{ to get the numbers of pairs } Step 2 – Add 1 to the last number ( 50 ) 1 + 50 = 51 { The sum of each pair is 51 } Step 3 – Multiply the results from steps 1 and 2 : 25 x 51 = 1275

Adding a Sequence of numbers (Pairing Method) Now you try : - 2. Find the sum of 1 + 2 + 3 ……. + 2518 + 2519 + 2520 What if the sequence of numbers that does not end with even numbers? Now you try : - 3. Find the sum of 1 + 2 + 3 ……. + 79 + 80 + 81 Now you try : - 4. Find the sum of 1 + 2 + 3 ……. + 2010 + 2011 + 2012 + 2013

Adding a Sequence of numbers (Triangle Method) 1. Find the sum of 1 + 2 + 3 ……. + 49 + 50 Problem Solving Strategy :- Step 1 – Multiply the last number (50) by the next higher number (51) and divide the product by 2. 50 x 51 ÷ 2 = 1275 Now you try : - 2. Find the sum of 1 + 2 + 3 ……. + 2518 + 2519 + 2520

Adding a Sequence of numbers (Average Method) What if the sequence of consecutive number does not start with 1? 1. Find the sum of 11 + 12 + 13 ……. + 49 + 50 Problem Solving Strategy :- Step 1 – Subtract the first number from the last number and add 1 (50 – 11) + 1 = 40{ to get the numbers of Terms } Step 2 – Add the first number to the last number and divide the result by 2. (11 + 50) ÷ 2 = 30.5 { The average is 30.5 } Step 3 – Multiply the results from steps 1 and 2 : 40 x 30.5 = 1220 Now you try : - 2. Find the sum of 4 + 5 + 6 ……. + 23 + 24+ 25

Adding a Sequence of numbers (Average Method) Now you try : - 3. Find the sum of 4 + 8 + 12 ……. + 36 + 40 + 44 Now you try : - 4. Find the sum of 7 + 14 + 21 ……. + 84 + 91 + 98

Adding a Sequence of odd numbers 1. Find the sum of 1 + 3 + 5 ……. + 49 + 51 Problem Solving Strategy :- Step 1 – Add 1 to the last number and divide the last number by 2 (1 + 51)÷ 2 = 26{ to get both the Average and the numbers of Terms } Step 2 – Square the results from step 1. 26 x 26 = 676 Now you try : - 2. Find the sum of 1 + 3 + 5 ……. + 195 + 197 + 199

Adding a Sequence of odd numbers What if the sequence of consecutive number does not start with 1? 1. Find the sum of 7 + 9 + 11 ……. + 31 + 33 Problem Solving Strategy :- Step 1 – Subtract the first number from the last number, divide it by 2 and add 1 (33 – 7) ÷ 2 + 1 = 14{ to get the numbers of Terms } Step 2 – Add the first number to the last number and divide the result by 2. (7 +33) ÷ 2 = 20 { The average is 20 } Step 3 – Multiply the results from steps 1 and 2 : 14 x 20 = 280 Now you try : - 2. Find the sum of 23 + 25 + 27 ……. + 41 + 43 + 45

Adding a Sequence of even numbers 1. Find the sum of 2 + 4 + 6 ……. + 48 + 50 Problem Solving Strategy :- Step 1 – Divide the last number by 2 50 ÷ 2 = 25{ to get the numbers of Terms } Step 2 – Add 2 to the last number and divide the sum by 2. (50 + 2) ÷ 2 = 26 {to get the average} Step 3 – Multiply the results from steps 1 and 2 25 x 26 = 650 Now you try : - 2. Find the sum of 2 + 4 + 6 ……. + 96 + 98 + 100

Adding a Sequence of even numbers What if the sequence of consecutive number does not start with 2? 1. Find the sum of 8 + 10 + 12 ……. + 32 + 34 Problem Solving Strategy :- Step 1 – Subtract the first number from the last number, divide it by 2 and add 1 (34 – 8) ÷ 2 + 1 = 14{ to get the numbers of Terms } Step 2 – Add the first number to the last number and divide the result by 2. (8 +34) ÷ 2 = 21 { The average is 20 } Step 3 – Multiply the results from steps 1 and 2 : 14 x 21 = 294 Now you try : - 2. Find the sum of 24 + 26 + 28 ……. + 52 + 54 + 56