Sum of Consecutive Integers
How
many integers from 10 to 40 can be written as the sum of 2 consecutive
integers?
How many integers from 10 to 40 can be written as the sum of 3 consecutive
integers?
How
many integers from 10 to 40 can be written as the sum of 4 consecutive
integers?
Can you find a pattern? Explain.
Problem setup
To
answer these questions, I began by figuring out the first number in the
sequence. For question 1, the
jump off point is 9 – but, 9 is not between 10 and 40, so I must
eventually throw this out.
Next, I continued from that point. Look at the illustration below:
I
noticed that the numbers are going up by 2. Therefore, with each multiple of 10,
there will be 5 numbers that adhere to this rule. For this question, I deduced that
there are 15 numbers that are the sum of two consecutive integers.
Now
for the next question.
As
you can see, my jump off point is 9 again; however, this time, the numbers
go up in increments of 3, and are multiples of 3! How fun! By continuing this pattern, I found
that there are 10 numbers that adhere to the rule, AND are between 10 and
40.
Third
question.
Now
this is a piece of cake! Notice
that the numbers increase by four with 10 as our starting point. There are 8 numbers that adhere to
our rule.
Plans to Solve/Investigate the Problem
Author & Contact.
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