Consecutive Numbers :: Papers

Consecutive Numbers Task 1 Problem 1 Write down 3 consecutive numbers. Square the middle one. Multiply the first and the third number. Compare the two numbers, what do you notice? Problem 2 ========= Write down two consecutive numbers. Square both of the numbers and find the difference between the squares. What do you notice? Problem 1 ========= I am going to investigate several sets of three consecutive numbers to see if the square of the middle is related to the product of the outer two numbers in any way. 9,10,11 10Â ²= 100 9x11= 99 3,4,5 I notice that the square of the middle number is always one more than the product of the other numbers. 4Â ²=16 3x5=15 18,19,20 19Â ²=361 18x20=360 1,2,3 2Â ²=4 1x3=3 30,31,32 31Â ²=961 30x32=960 1st Number 2nd Number 3rd Number 2nd number squared 1st number x 3rd number 9 10 11 100 99 3 4 5 16 15 18 19 20 361 360 1 2 3 4 3 30 31 32 961 960 I have put my results in a table so that they will be easier to analyse and compare. When you take three consecutive numbers, square the middle and multiply the outer two, the squared number will always be one more than the product of the outer two. If this rule is correct, then by using the three consecutive numbers: 101,102,103, I predict that 102Â ² will equal one more than 101x103. 101,102,103 102Â ²=10404 101x103= 10403 My prediction was correct as 102Â ², 10404, is one more than 101x103, 10403.