Q&A for How to Add Consecutive Integers from 1 to 100

See Sum the Integers from 1 to N.

You need to know how many consecutive numbers you are looking for and then use algebra to solve. For example, if you know you are looking for 5 numbers, you would set up the equation x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 100. Then, simplify: 5x + 10 = 100; 5x = 90; x = 18. So, the five consecutive numbers are 18, 19, 20, 21, and 22.

Let n be the first number, so that (n + 1) is the number you're looking for. The problem can be stated as (n) + (n+1) + (n+2) + (n+3) = 50. Combining terms, 4n + 6 = 50. Then 4n = 44, and n = 11. That means the number you're looking for is 12.

Let n be the first number and (n+1) the second number. Then (n) + (n+1) = 151. Combining terms, 2n + 1 = 151. Then 2n = 150, and n = 75. So the two numbers are 75 and 76.

The volume is (x + 1)³ = (x + 1)(x + 1)(x + 1) = x³ + 3x² + 3x + 1.