Consecutive Numbers
Task 1
Problem 1
Write down 3 consecutive numbers. Square the middle one. Multiply the
first and the third number. Compare the two numbers, what do you
notice?
Problem 2
=========
Write down two consecutive numbers. Square both of the numbers and
find the difference between the squares. What do you notice?
Problem 1
=========
I am going to investigate several sets of three consecutive numbers to
see if the square of the middle is related to the product of the outer
two numbers in any way.
9,10,11
10²= 100
9x11= 99
3,4,5
I notice that the square of the middle number is always one more than
the product of the other numbers.
4²=16
3x5=15
18,19,20
19²=361
18x20=360
1,2,3
2²=4
1x3=3
30,31,32
31²=961
30x32=960
1st Number
2nd Number
3rd Number
2nd number squared
1st number x 3rd number
9
10
11
100
99
3
4
5
16
15
18
19
20
361
360
1
2
3
4
3
30
31
32
961
960
I have put my results in a table so that they will be easier to
analyse and compare.
When you take three consecutive numbers, square the middle and
multiply the outer two, the squared number will always be one more
than the product of the outer two.
If this rule is correct, then by using the three consecutive numbers:
101,102,103, I predict that 102² will equal one more than 101x103.
101,102,103
102²=10404
101x103= 10403
My prediction was correct as 102², 10404, is one more than 101x103,
10403.
The results of this experiment are shown in the compiled student data in Table 1 below.
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