Is there a name for this "effect"?

[Gawdzilla Sama]

This picture points out something I actually learned on my own. I also noticed that adding the two digits of each result produced an interesting additional "effect".

378989_363786467041858_1484511603_n.jpg (31.02 KiB) Viewed 5163 times

[FBM]

"Bob."

[HomerJay]

"Maffs"

[Gawdzilla Sama]

"Maffs"

/thread

[pErvinalia]

miracle

[pErvinalia]

or irreducible complexity stuff...

[rasetsu]

I don't know that there's an effect here as there's no underlying generative phenomenon that applies to other series. The fact that it's close to 10 guarantees that for long stretches of the series, the tens digit will count upward by one each time. The fact that it is one less than 10 guarantees that the ones place will decreases by one each time. The two combined result in the sum being constant in that stretch of the series. Note the following terms, 90, 99, 108, 117, 126... it hiccups at the crossover at 99.

However this is certainly not the only series with interesting properties of course. One trick they teach you in order to understand series behavior like they show on tests is to lay the numbers out at top, then find the difference between each term. If that isn't constant, find the difference between those terms and so on until you reach a constant. Another thing to note is multiplicative patterns. This is done by breaking the series down in to prime factors. So for example, your series would be:

54 -- 63 -- 72
9x6 -- 9x7 -- 9x8
(3 x 3) x 6 -- (3 x 3) x 7 -- (3 x 3) x 8
(3 x 3) x (2 x 3) -- (3 x 3) x 7 -- (3 x 3) x (2 x 2 x 2)

Note, looking at the commonalities here, we could build the series:

36 -- 72 -- 144 -- 288

Which would be:
36 -- 72 -- 144 -- 288 =
(3 x 3) x (2 x 2) -- (3 x 3) x (2 x 2 x 2) -- (3 x 3) x (2 x 2 x 2 x 2) -- (3 x 3) x (2 x 2 x 2 x 2 x 2)

Which if we subtract out is:
36 -- 72 -- 144 -- 288 =
36 -- 72 -- 144
36 -- 72
36

so 36, or (3 x 3) x (4 x 4) is the common denominator in the series, being 36 x 1, x 2, x 4 difference at each term.

[klr]

This picture points out something I actually learned on my own. I also noticed that adding the two digits of each result produced an interesting additional "effect".

378989_363786467041858_1484511603_n.jpg

"Three is the magic number". Old numerology is old.

[Mysturji]

Not only that, but every multiple of nine adds up to 9 when you add up the individual digits. (handy for checking your sums)
At least, that's true up to 108. After that I got bored and wandered off.

[Mysturji]

Try doing that in hexadecimal.
Let me know how that works out for you.

[rasetsu]

Try doing that in hexadecimal.
Let me know how that works out for you.

9 - 12 - 1B - 24 - 2D - 36 - 3F - 48 - 51

Note the following two facts with every other term starting with the second term:
a) the difference is 12 (decimal 18)
b) the sum of the digits is a series, 3 - 6 - 9 - 12 (hexadecimal 0C)

[Tero]

It's a pairofdimes, a variant of paradigm.

[Robert_S]

I just call it the Pattern of the Nines.

Trying to memorize the multiplication table was painful for me until someone pointed out some of the patterns. The only rows/columns that you really need to memorise are the 2's 3's and 7*7. Once you can double a number, you have the 2's 4's and 8's down by repeating the doubling process. Once you can triple a number, you can also get the 6's by tripling then doubling or vice versa. The only hole left is 7*7. All you have to remember is that that number is 62 and you're all set.

[Audley Strange]

"The Proof of God as Eternal Trinity Indivisible."

Base 10 numerical Symbol Deficit.

[Kristie]

This picture points out something I actually learned on my own. I also noticed that adding the two digits of each result produced an interesting additional "effect".

378989_363786467041858_1484511603_n.jpg

Teachers do so teach that! My daughter thought she was teaching me something new when she told me about it weeks ago!