The average of all odd numbers from 3 to 3135 is （3+3135）/2=1569

　　The average of all multiples of 7 from 14 to 126 is （14+126）/2=70

　　remember：

　　Make sure no number is missing in the middle.

　　With more numbers， average of an ascending AP increases.

　　With more numbers， average of a descending AP decreases.

　　AP:numbers from sum

　　given the sum s of m numbers of an AP with constant increment d， the numbers in the set can be calculated as follows：

　　the first number x = s/m - d（m-1）/2，and the n-th number is s/m + d（2n-m-1）/2.

　　Example：

　　if the sum of 7 consecutive even numbers is 70， then the first number x = 70/7 - 2（7-1）/2 = 10 - 6 = 4.

　　the last number （n=m=7）is 70/7+2（27-7-1）/2=10+6=16.the set is the even numbers from 4 to 16.

　　Remember：

　　given the first number x， it is easy to calculate other numbers using the formula for n-th number： x+（n-1）

　　AP:numbers from average

　　all m numbers of an AP can be calculated from the average. the first number x = c-d（m-1）/2， and the n-th number is c+d（2n-m-1）/2， where c is the average of m numbers.

　　Example：

　　if the average of 15 consecutive integers is 20， then the first number x=20-1（15-1）/2=20-7=13 and the last number （n=m=15） is 20+1（215-15-1）/2=20+7=27.

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