Question

the average of 4 consecutive odd number is 8 less than the average of 3 consecutive Even numbers. some of 4 odd numbers is equal to some of 3 even numbers.
find some of 4 consecutive odd numbers
a) 120
b) 130
c) 128
​

Answer 1

Answer:

Step-by-step explanation:

The average of evenly spaced set with even number of terms (4 in our case) is the average of two middle terms.

The average of evenly spaced set with odd number of terms (5 i our case) is the middle term.

Say the average of 4 consecutive odd numbers is xx and the average of 5 consecutive even numbers is yy.

Given: x=y2x=y2 and x+y=18x+y=18 --> solve for xx and yy: x=6x=6and y=12y=12.

So, we have that the average of 4 consecutive odd numbers is 6, which means that those numbers are: {3, 5, 7, 9} (6 is the average of two middle terms);

Similarly we have that the average of 5 consecutive even numbers is 12, which means that those numbers are: {8, 10, 12, 14, 16} (12 is the middle term);

The difference between the largest and smallest of these numbers is 16-3=13.