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(2*7-7-1)/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 www.examw.com
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*(2*15-15-1)/2=20+7=27.
if the average of 33 consecutive odd numbers is 67, then the first number x=67-2*(33-1)/2=67-32=35 and the last number (n=m=33) is 67+2*(2*33-33-1)/2=67+32=99.
Remember:
sum of the m numbers is c*m,where c is the average.
