The average of all odd numbers from 3 to 3135 is /2=1569
The average of all multiples of 7 from 14 to 126 is /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/2,and the n-th number is s/m + d/2.
Example:
if the sum of 7 consecutive even numbers is 70, then the first number
x = 70/7 - 2/2 = 10 - 6 = 4.
the last number is 70/7+2/2=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+
AP:numbers from average
all m numbers of an AP can be calculated from the average. the first number
x = c-d/2, and the n-th number is c+d/2, where c is the
average of m numbers.
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