Thread: Pattern.... squares

52 (squared 2) = 25
152 (squared 2) = 225
252 (squared 2) = 625
352 (squared 2) = 1225
452 (squared 2) = 2025
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What is the pattern or rule that links the underlined part of the number that is squared and the underlined part of its value?

Using the pattern from Part b above, write down the answer to 952 (2 is squared, like the little 2). Show your working.

Originally Posted by Sazza

52 (squared 2) = 25
152 (squared 2) = 225
252 (squared 2) = 625
352 (squared 2) = 1225
452 (squared 2) = 2025
-----------------------
What is the pattern or rule that links the underlined part of the number that is squared and the underlined part of its value?

Using the pattern from Part b above, write down the answer to 952 (2 is squared, like the little 2). Show your working.

Note, if we want to write sqaured, or any other power for that matter, we use "^"

so 5 squared is typed as 5^2

Now, we want to figure out a pattern that links the underlined numbers. so let's write them out in a table:

let n represent the number that is underlined in the sqaured number
let f(n) be the function the relates it to the evaluated number

....n..............................f(n)
---------------------------------------
....1...................2 = 1*2 = 1*(1 + 1)
....2...................6 = 2*3 = 2*(2 + 1)
....3...................12 = 3*4 = 3*(3 + 1)
....4...................20 = 4*5 = 4*(4 + 1)
.
.
.
....n...................?

what do you think the general formula is?

Well i'v noticed that: in the brackets, it's well for example you had: 2 = 1 * 2 = 2* = 1*(1+1)
* means multiply right? Well in that case, we multiply the 2 by 1 which gives us one, but before the 2*1 it's kinda explanation. (1+1) equals 2, times 1 equals 2, and well where you have the 2*1=2, your just showing it, in normal equation format.
The General Formula?

Originally Posted by Sazza

Well i'v noticed that: in the brackets, it's well for example you had: 2 = 1 * 2 = 2* = 1*(1+1)
* means multiply right? Well in that case, we multiply the 2 by 1 which gives us one, but before the 2*1 it's kinda explanation. (1+1) equals 2, times 1 equals 2, and well where you have the 2*1=2, your just showing it, in normal equation format.
The General Formula?

you sound confused

okay. you notice in the second column, that in the brackets we add a 1 no matter what, so that does not depend on what line we are at. so let's not concentrate on that too hard. let's see where the numbers repeat them selves.

notice, for the second column of line 1 we have:
1*(1 + 1)

for the second column of line 2 we have:
2*(2 + 1)

for the second column of line 3 we have:
3*(3 + 1)

and so on.

it means for the nth line, we have:
n*(n + 1)

so the general formula is: f(n) = n(n + 1) where n is the line we are at and f(n) gives the number in front of 25

now try to figure out what 95^2 is

95>2=




90=9*10=9*(9 + 1)

Originally Posted by Sazza

95>2=




90=9*10=9*(9 + 1)

did you look at the pattern? and the sign should be "^" not ">"

remember, the n(n + 1) only gives the digit in front of the 25.

so for 95^2, the number in front of 25 is given by: 9(9 + 1) = 9*10 = 90

so, 95^2 = 9025

Yep i couldn't find the ^ but i found it now.
Ah so the number in front of 25 is given by: 9(9 + 1) = 9*10 = 90?
Okay...
so, 95^2 = 9025

Originally Posted by Sazza

Yep i couldn't find the ^ but i found it now.
Ah so the number in front of 25 is given by: 9(9 + 1) = 9*10 = 90?
Okay...
so, 95^2 = 9025

yeah, which is what i said, but you have to look at the pattern to figure that out. remember our pattern is only for the underlined numbers. if you look in the original table you posted, there is always a 25 after the underlined number on the right. and the underlined number on the right is given by the pattern n(n + 1), where n is the underlined number on the left