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Thread: hard Sequence and Series Question!!

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    hard Sequence and Series Question!!

    Its probably under harder 2unit in extension 1 but here's the question! please help

    1,3,6,10,15....are called triangular numbers

    Use the formula for the sum of an arithmetic series to find the 30th triangular number.
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    Re: hard Sequence and Series Question!!

    Quote Originally Posted by kevda1st View Post
    Its probably under harder 2unit in extension 1 but here's the question! please help

    1,3,6,10,15....are called triangular numbers

    Use the formula for the sum of an arithmetic series to find the 30th triangular number.
    1 = 1
    3 = 1+2
    6 = 1 + 2 + 3
    10 = 1 + 2 + 3 + 4

    30th number will be

    30/2 (2 + 29 x 1 ) = 465

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    Re: hard Sequence and Series Question!!

    1, 3, 6,10,15,.......

    New set of series you can make from top
    1+2+3+4+5+6+......
    true since 1+2 = T2 from original
    1+2+3 = T3 from original
    1+2+3+4 = T4 (" ")
    so on....

    a= 1 n=30 d= 1

    s30= 30/2 (2x1+(30-1)x1)
    = 15x31
    = 465

    lol kev, cya
    Last edited by ghostman_on_3rd; 6 Apr 2009 at 1:03 PM.
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    Question Re: hard Sequence and Series Question!!

    Quote Originally Posted by ghostman_on_3rd View Post
    1, 3, 6,10,15,.......

    New set of series you can make from top
    1+2+3+4+5+6+......
    true since 1+2 = T2 from original
    1+2+3 = T3 from original
    1+2+3+4 = T4 (" ")
    so on....

    a= 1 n=30 d= 1

    s30= 30/2 (2x1+(30-1)x1)
    = 15x31
    = 465

    lol kev, cya
    Sorry, I know this was a post a LOOONNGG time ago but why is d=1? Though you did say you made a replica series with 1+2+3+4+5... but may I ask of how exactly you derived that? If anyone passing this knows, please reach out. I'm sorry if it's a intuitive question, I just don't get the reasoning behind it yet. Thanks!

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    Re: hard Sequence and Series Question!!

    Quote Originally Posted by orwellstudent View Post
    Sorry, I know this was a post a LOOONNGG time ago but why is d=1? Though you did say you made a replica series with 1+2+3+4+5... but may I ask of how exactly you derived that? If anyone passing this knows, please reach out. I'm sorry if it's a intuitive question, I just don't get the reasoning behind it yet. Thanks!


    (1 layer) T1 = 1:



    (2 layers) T2 = 3:

    ••

    (3 layers) T3 = 6:

    ••
    •••

    (4 layers) T4 = 10:

    ••
    •••
    ••••

    (5 layers) T5 = 15:

    ••
    •••
    ••••
    •••••,

    Last edited by InteGrand; 5 Jan 2019 at 12:48 AM.

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