Sunday, October 2, 2011

Blog Post 5D

Sequences are just numbers in a particular order. Look at the sequence of odd numbers.

1,3,5,7,9,...

Add up parts of the sequence...

1 + 3 = ??

1 + 3 + 5 = ???

1 + 3 + 5 + 7 = ???

What do you notice?

Now subtract any two consecutive numbers.
3 - 1 = ??

9 - 7 = ??

15 - 13 = ??

What do you notice?

Both of these facts are not a coincidence and, actually have a lot to do with the way objects fall to the ground. We will study this next semester.
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17 comments:

  1. Misbah.TOctober 5, 2011 at 4:30 PM

    1+3 is 4
    1+3+5 is 9
    1+3+5+7 is 16

    they are all perfect squares.
    even if you continue the pattern.
    1+3+5+7+9 is 25
    which would be the next square.

    by subtracting any two consecutive numbers you always end up with 2.

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  2. Avery F.October 6, 2011 at 11:51 AM

    Yeah i agree. 4, 9 and 16 are the answers, and they are all perfect squares. In the second set of problems are...

    3 - 1 = 2
    9 - 7 = 5
    15 - 13 = 2

    My guess is that they will repeat like this forever

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  3. Fabiola.MOctober 6, 2011 at 12:38 PM

    The sequence on the odd problems was that you kept on adding by 2 and so the numbers that you would get at the end would be perfect squares like the root of 4 is 2 and the root of 16 is 4 and so on, so no matter what the answer was, they would just be perfect squares if you keep on adding by the 2. On the subtraction problems you would just get 2 as your answers and it would not matter the number you would subtract cause you would end up with two.

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  4. Yajaira, HOctober 6, 2011 at 12:49 PM

    I agree with both answers, but Avery you made a mistake 9-7 = 2 , but just like they said when you keep adding odd numbers together your going to end up with perfect squares & Subtracting numbers keeps giving you two like when you subtract 25-23 you get 2

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  5. Ladi A.October 6, 2011 at 12:58 PM

    I agree with everyone else, and I noticed the same thing. When you add the odd numbers in a particular order, you always get a perfect square. 4,9,16,25,36,etc. Also when you subtract the odd numbers that are consecutive you always get 2 forever and ever. It is really interesting how when you add the odd number sequences, you always get a perfect square. Maybe because each number is 2 units apart 1,3,5,7,9,11.

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  6. DoreenKOctober 6, 2011 at 1:53 PM

    yes i agree with the others,
    4,9, and 16 are all perfect squares.
    (4,9,16,25,36,49 ...)
    But when you subtract any two of the consecutive odd numbers, you end up with two. (15-3=2, 3-1=2, and 9-7=2)

    ReplyDelete
  7. greeneyedmistressOctober 6, 2011 at 2:16 PM

    everyone is right, when you add each problem you get
    1 + 3 = 4
    1 + 3 + 5 = 9
    1 + 3 + 5 + 7 = 16
    i noticed each answer you get is a perfect square.
    and if you keep going, and add "9" you get 25, which is also a perfect square.
    Also, this has a lot to do with objects falling to the ground [connecting with physics much? lol] Galileo discovered that math has to do with motion.
    He discovered, as you go from one second to the next, the ball rolls down the plane, the ratios of the distances covered increase by odd numbers, by intervals of 1, 3, 5, 7, 9, etc. -->which show that the odd sequence has to do with motion.

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  8. TariroOctober 6, 2011 at 3:41 PM

    1 + 3 = 4

    1 + 3 + 5 = 9

    1 + 3 + 5 + 7 = 16

    3 - 1 = 2

    9 - 7 = 2

    15 - 13 = 2

    I noticed that the first three equations result in numbers that are perfect squares, and the numbers added go up in intervals of 2. Also, all the numbers you're adding together to get the perfect square are odd numbers, which I think is pretty cool! I think if you keep going up in intervals of 2 for the numbers you're adding together(and they're odd), you'll keep getting perfect squares.

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  9. Munira BOctober 6, 2011 at 4:46 PM

    1,3,5,7,9,...
    All the numbers have a difference of 2.
    They are all prime numbers.

    Add up parts of the sequence...

    1 + 3 =4

    1 + 3 + 5 = 9

    1 + 3 + 5 + 7 = 16

    The numbers are all perfect squares.
    Have a pattern even then odd then even and then odd. So forth..
    1+3+5+7+9=25
    Is an odd number odd compared to the prior number 16 which is even.

    3 - 1 = 2

    9 - 7 = 2

    15 - 13 = 2

    all of the answers are two.
    21-19=2

    ReplyDelete
  10. CamiOctober 6, 2011 at 6:26 PM

    1,3,5,7,9,
    ^ they're all prime numbers and the rule is to add 2 each time


    1 + 3 = 4

    1 + 3 + 5 = 9

    1 + 3 + 5 + 7 = 16

    ^I noticed that all these add up to be perfect squares because
    2x2=4 , 3x3=9, and 4x4=16 and if you keep going it's endless perfect squares.. for example:
    1+3+5+7+9+11+13+15= 49


    Now subtract any two consecutive numbers.
    3 - 1 = 2

    9 - 7 = 2

    15 - 13 = 2

    the difference of all the numbers is 2 because that's the rule between the first set of numbers given (1,3,5,7,9) It's just the same math but backwards in a way.

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  11. Theresa N.October 6, 2011 at 8:28 PM

    1,3,5,7,9,..
    1+2=3
    3+2=5
    5+2=7
    7+2=9
    The difference is two for this sequence.


    1 + 3 = 4

    1 + 3 + 5 = 9

    1 + 3 + 5 + 7 = 16
    they're all perfect squares and the pattern goes from even to odd.

    ReplyDelete
  12. Olivia O.October 6, 2011 at 9:14 PM

    1 + 3 = 4

    1 + 3 + 5 = 9

    1 + 3 + 5 + 7 = 16

    I noticed that these three numbers are both perfect squares and prime numbers.
    2x2 = 4 3x3 = 9 4x4 = 16
    If you keep adding 2 to the sequence, the answers will still be perfect squares.


    3 - 1 = 2

    9 - 7 = 2

    15 - 13 = 2

    Theres really no pattern, it's just a repetitive answer.All the numbers being subtracted are odd numbers. This shows that if you're subtracting odd numbers, the answer will come out even. For example, 11 - 3 = 8 <-- positive # , 21 - 17 = 4 <-- positive #, etc.

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  13. Toye O.October 7, 2011 at 6:40 PM

    Sorry for the late post i was confused as to what we had to comment on. I noticed that if you continue the pattern your answer will always come out to be a perfect square. But how and what does this have to do with the way objects fall to the ground?

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  14. Thien V.October 7, 2011 at 9:30 PM

    There is a difference of 2 in each of the first sequences. also they are perfect squares.

    For the second set of problems, all of them are 2, and when subtracting 2 odd numbers together, you may end up with an even number.

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  15. Hector P.October 8, 2011 at 12:31 PM

    ok so if you keep adding the consecutive numbers together you will get perfect squares, so will this work when you add any number that is consecutive? and will the same happen with the subtraction of any 2 consecutive numbers! so far its true dough, that by adding those it will give you a perfect square and by subtracting it, it will be 2!!!

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  16. michaelOctober 9, 2011 at 6:30 AM

    1+3=4

    1+3+5=9

    1+3+5+7=16

    I really don't see anything but if you keep add and jump to the next two numbers you will get perfect squares.

    3-1=2

    9-7=2

    15-13=2

    i noticed that just keep add and you will get perfect square and keep subtracting and you will keep repeating the same number 2

    ReplyDelete
  17. NikolKOctober 10, 2011 at 5:28 PM

    1+3=4
    1+3+5=9
    1+3+5+7=16

    all of the above are perfect squares.

    3-1=2
    9-7=2
    15-13=2

    im totally guessing but ive noticed that the numbers above are similar to the addition numbers. theres some pattern going on with odd and even numbers that i cannot figure out...

    this is late.... i know.

    ReplyDelete

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