(2n)2 + (2n+1)2 = 4n2 + 4n2 + 2n + 2n + 1 = 8n2 + 8n + 1 = 8(n2 + n) + 1 Anything multiplied by 8 will be even. Add 1 makes it odd. Mark Ravenwood Folkestone School for Girls
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Consecutive even numbers are any even numbers which are separated by one (uneven) number... so that 6 and 8 are consecutive even numbers... as are 22, 24 and 26. Similarly, consecutive odd numbers are numbers which are separated by one (even) number... so that 11 and 13 are consecutive odd numbers... as are 31, 33 and 35.
This answer cannot be answered because two consecutive numbers consist of one odd number and one even number, and the sum of an odd number plus an even number is always an odd number.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, the number 15 can be written as the sum of consecutive integers in three different ways: 15=7+8 15=4+5+6 15=1+2+3+4+5 Look at numbers other than 15 and find out all you can about writing them as sums of consecutive whole numbers.
Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number.
-- method -- We need X numbers which are consecutive, so the middle number will be 1/ X of the total. Divide the sum of the numbers by the number of numbers ... in this case divide 186 by 3. The numbers are to be consecutive and even, so subtract 2 from the number go get one of the numbers and add 2 to the number to get the other number. You now have three numbers which are even and consecutive. Now, place a minus sign in front of them, to turn them into negative numbers For instance 12, 14 and 16 are three consecutive numbers whose sum is 42. -12, -14 and - 16 are three consecutive even integers whose sum is -42 Now you know all you need to solve the problem.