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Math Help - arithmetic sequence

  1. #1
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    arithmetic sequence

    Meredith starts a saving fund for her son. She deposits $10 on his first birthday, $20 on his second, $30 on his third and so on....for 40 years (wow, is he still going to be living with her, too? Lol *ahem*....).

    Use t_{n}=a+(n+1)d to determine how much she will have deposited in total (ignore interest at this point).

    I don't understand how to plug this into the formula, example:

    t_{3}=10+(30+1)(10), which equals $320, but logic tells me that $10 + $20 +30, only equals $60.

    What am I missing?
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  2. #2
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    Hello, sux@math!

    Meredith starts a saving fund for her son. She deposits $10 on his 1st birthday,
    $20 on his 2nd, $30 on his 3rd, and so on for 40 years.

    Use t_{n}=a+(n+1)d . . . . No!
    That's not the formula . . . In fact, it's not any formula!


    The sum of the first n terms of an arithmetic series is:
    . . S_n \;=\;\frac{n}{2}\bigg[2a + (n-1)d\bigg]


    Now try it with: . n = 40,\;a = 10,\;d = 10

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  3. #3
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    Hi Soroban!

    That first formula, could it be a typo and it should read n-1? That's the closest thing I can find in my book and it is the one on my pre-test sheet that they have given me....

    BUT the formula you gave is RIGHT! It works on every term I have tried! THANK YOU!
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  4. #4
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    And Soroban, can you help with part 2?

    If Meredith's first deposit of $10 earns 5% interest, compounded monthly, what will the final deposit be?

    Will it work if I tack on the end of that formula you gave me:

    +0.05^{n}, where n=40?
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  5. #5
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    Actually, n=480, correct? Because it will be 12 x 40?
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