Sum of Four Consecutive Integers

How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers?
Source: NCTM Mathematics Teacher

SOLUTION
1+2+3+4=10
2+3+4+5=14
3+4+5+6=18
4+5+6+7=22
5+6+7+8=26
6+7+8+9=30
7+8+9+10=34
8+9+10+11=38
9+10+11+12=42
10+11+12+13=46
11+12+13+14=50
\dots
The pattern is 10,30,50,\dots These multiples of 10 when plotted on a number line are separated by an interval of 20. How many intervals of 20 are there from 10 to 999?
999\div 20=49.95
The number of multiples of 10 that are the sum of four consecutive integers
49+1=50

Answer: 50

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About mvtrinh

Retired high school math teacher.
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