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.
Example:
if the average of 15 consecutive integers is 20, then the first number x=20-1/2=20-7=13 and the last number is 20+1/2=20+7=27.
if the average of 33 consecutive odd numbers is 67, then the first number x=67-2/2=67-32=35 and the last number is 67+2/2=67+32=99.
Remember:
sum of the m numbers is cm,where c is the average.
以上是为大家整理的新GRE数学重要考点知识,希望能给新GRE考生带来一定的帮助。
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