How to Find & Describe Consecutive Integers
- 1). Set up word problems involving consecutive numbers using only one variable and adding one for each new number in the sequence. For example, a typical problem might be: "Find five consecutive numbers that sum to 75." One way to set up the problem is N + (N + 1) + (N + 2) + (N + 3) + (N + 4) = 75; 5N + 10 = 75; 5N = 65; N = 13. So the numbers are 13, 14, 15, 16 and 17. Another way to set up the problem is (K - 4) + (K - 3) + (K - 2) + (K - 1) + K = 75; 5K - 10 = 75; 5K = 85; K = 17. Once again the numbers are 13, 14, 15, 16 and 17.
- 2). Do problems that involve consecutive odd or consecutive even numbers by incrementing the variables with a two each time. For example, suppose the problem states, "The sum of 10 consecutive even numbers is 110. What is the largest of the numbers?" This time it is preferable to let "X" be the last number, so (X - 18) + (X - 16) + (X - 14) + (X - 12) + (X - 10) + (X - 8) + (X - 6) + (X - 4) + (X - 2) + X = 110. So 10X - 90 = 110; 10X = 200; X = 20.
- 3). Find the sum of the first and last numbers in a sequence by the formula N + (N + K) where "N" is the first number in the sequence and "K" depends on the length of the sequence and the size of the step between elements in the sequence. A typical word problem is: "What is the sum of the first and third even numbers with three digits?" This would be 102 + 106 = 208.
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