Question 1123041: The sum of 5 consecutive integers is 505.
what is the third number in this sequence? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52803) (Show Source):
The quick answer given by tutor @ikleyn uses a shortcut that is often useful in problems involving arithmetic sequences. (An arithmetic sequence is a sequence of numbers in which there is a constant difference from one number to the next. A sequence of consecutive integers is a common example.)
Because of the equal spacing between the numbers in an arithmetic sequence, the middle number is the average of all the numbers. In a sequence of 5 numbers, the 3rd number is the middle number.
So in your problem the third number is the average of the 5 numbers -- which is the sum of the numbers, divided by how many there are: 505/5 = 101.
