posted by Max

I swear, last question!

Calculate S(31) for the arithmetic sequence in which a(9) = 17 and the common difference is d = -2.1


Usually, I can figure these out but I'm stuck:(

  1. Arora

    a(n) = a(1) + (n-1)d
    a(9) = a(1) + (9-1)d

    You have a(9), you have d
    Use those to get a(1) from the above mentioned.

    Then, plug those values into the sum formula I mentioned on the other question.

  2. Max

    Ok, I'm so sorry, but I got so lost.
    For some reason, (I think) I'm getting it wrong at determining a(1).
    I don't know what the heck I'm doing, but I've gotten either 5.9, -5.9, or 11.1 for a(1) and none of them work for the other formula. I feel super dumb right now, is there any chance you could show me again how to get a(1)? Sorry

  3. Max

    Wait-- I made a dumb typo. I think it's 71.3 (oh my gosh I'm dying)

  4. Arora

    a(9) = a(1) + (n-1)d
    a(9) = 17, d = -2.1

    17 = a(1) + (9-1)*-2.1
    a(1) = 17 + 16.8
    = 33.8

    S(31) = (n/2)[2a(1) + (n-1)d]
    = (31/2)[2(33.8) + 30(-2.1)]
    = (31/2)(67.6 - 63)
    = (31/2)(4.6)
    = 31*2.3
    = 71.3

    Yes, you're correct

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