Geometric series

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  1. Geometric series formula:sn=t1  (rn−1)r−1{s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}
    Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … .
    1. Geometric series formula: sn=r⋅tn−t1r−1s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}
      Determine the sum of the geometric series: 8 + 2 + 12\frac{1}{2} + …. + 1512\frac{1}{{512}} .
      1. A tennis ball is dropped from the top of a building 15 m high. Each time the ball hits the ground, it bounces back to only 60% of its previous height. What is the total vertical distance the ball has travelled when it hits the ground for the fifth time?
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        Topic Notes
        A geometric series is the sum of a finite number of terms in a geometric sequence. Just like the arithmetic series, we also have geometric series formulas to help us with that.
        The sum of  n  \, n\, terms of a geometric series:

        Sn=t1(rn−1)r−1=r⋅tn−t1r−1\large S_n = \frac{t_1(r^{n}-1)} {r-1} = \frac{r \cdot t_{n} - t_{1}} {r-1}