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    A geometric progression has first term 20 and common ratio 0.9. Find the sum of the first 30 term. How do i do this?
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    (Original post by Chelsea12345)
    A geometric progression has first term 20 and common ratio 0.9. Find the sum of the first 30 term. How do i do this?
    a= 20, r = 0.9 and you have a formula for the sum of the first n terms (I believe its in the formula book,so you dont even have to learn it off, although double check this as im not sure)

    its  \displaystyle S_n = \frac{a(r^n -1)}{r-1}
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    (Original post by DylanJ42)
    a= 20, r = 0.9 and you have a formula for the sum of the first n terms (I believe its in the formula book,so you dont even have to learn it off, although double check this as im not sure)

    its  \displaystyle S_n = \frac{a(r^n -1)}{r-1}

    Our tip is to also learn the proof of the formula since examiners like to ask for this quite often.

    It is:

    Sn = a + ar + ar^(2) + .. + ar^(n-1)

    Then multiply by r:

    rSn = ar + ar^(2) + ... + ar^(n)

    Take one from the other: Sn - rSn = a + ar^(n)

    Factorise both sides: Sn (1 - r) = a(1- r^(n))

    Which gives the formula after solving for Sn.
 
 
 
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