1/2, 2, 4 1/2, 8, 1 1/2…
This is from my sixth grader’s math homework. Seems kinda tough to me.
If the last number is 12-1/2,…
1/3, 4/2, 9/2, 16/2, 25/2…
Does that help?
If the last number really is 1-1/2, I dunno.
Sorry – typo in the spoiler box – first number s/b 1/2, as you gave it.
shouldn’t the 5th entry be 12 1/2? if so the pattern is +1 1/2, +2 1/2, +3 1/2, +4 1/2 etc…
the eigth entry should be 32 I think.
The difference between terms is 1 1/2, 2 1/2, 3 1/2 …
So the series is:
1/2
2
4 1/2
8
12 1/2
18
24 1/2
32
Hey, wait a minute. Did you make a typo?
This seems like the most logical answer to me. I think there is a typo in the book.
Each term n could also be represented as n[sup]2[/sup] / 2.
The pattern is:
Start with 0, 2 and 4 as seeds. Each number following these first three is generated from the number two previous to itself, by multiplying that previous number by a certain number M. M is a number generated by iteration at each step from M’s value as generated at the previous step. M begins at four, and at each step takes on the value equal to its previous value minus one. So the fourth number is generated from the second number by multiplying it by four, while the fifth number is generated from the third number by multiplying it by three. The sixth number will be generated from the fourth number (8) by multiplying it by 2.
Having generated this series, tack on 1/2 to every other number, starting with the first number in the series, 0.
So, the next few numbers in the series are 16, 12.5, 0, -12.5, 0, -36.5, 0, -180.5, and so on.
And now for something completely not different, but sort of not the same:
‘Wittgenstein begins his exposition by introducing an example: " … we get [a] pupil to continue a series (say + 2) beyond 1000 – and he writes 1000, 1004, 1008, 1012 (PI 185)". What do we do, and what does it mean, when the student, upon being corrected, answers “But I went on in the same way”? Wittgenstein proceeds (mainly in PI 185-243, but also elsewhere) to dismantle the cluster of attendant questions: How do we learn rules? How do we follow them? Wherefrom the standards which decide if a rule is followed correctly? Are they in the mind, along with a mental representation of the rule? Do we appeal to intuition in their application? Are they socially and publicly taught and enforced? In typical Wittgensteinian fashion, the answers are not pursued positively; rather, the very formulation of the questions as legitimate questions with coherent content is put to the test.’ --Stanford Encyclopedia of Philosophy
-FrL-
I don’t know where Frylock came up with such a perverse rule. The answer practically leaps out at you. To find the nth term, just take the difference of the previous two terms, add the previous term, and then subtract (11/2)n[sup]2[/sup] − (77/2)n + 65. So the sixth term is −37, followed by −140.5, −353, and −729.5.
My favourite series, with a very nice rule, is:
0, 1, 2, …
I maintain that the next number in the series is approximately 2.601218944 x 10^1746.
The rule is that each term is n followed by n factorial signs:
0 = 0
1 = 1!
2 = 2!!
and the next term is 3!!!, or 6!!, or 720!
After that, the terms get really big.
LOL…can’t believe I said that about a math example. I’m sure it would be wasted on his teacher
Sorry, I missed something: What is it you said about a math example which you can’t believe you said?
-FrL-
That was funnier than the last three Steve Martin movies combined. Either that, or I’m a complete nerd. (Probably both.)
Thanks…I need that. Now, back to configuring Samba…
Stranger