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8.05 Geometric series

Interactive practice questions

A ball dropped from a height of $24$24 metres will bounce back off the ground to $60%$60% of the height of the previous bounce (or the height from which it is dropped when considering the first bounce).

a

Write a function, $y$y, to represent the height of the $n$nth bounce.

b

Find the height of the fifth bounce. Give your answer correct to two decimal places.

Medium
2min

When a ball is dropped onto a horizontal surface from a height of $6$6 metres, it reaches a vertical height of $50%$50% of the starting height on its first bounce. It continues to reach a height of $50%$50% of the previous height in each subsequent bounce.

Hard
4min

When a marble is rolled horizontally on a flat surface it rolls $30$30 cm in the first second. It then rolls $60%$60% of the distance travelled in the previous second, for each subsequent second.

Hard
3min

Consider the series $8+1+\frac{1}{8}$8+1+18​$\dots$…

Find the sum of the first $7$7 terms. Round your answer to three decimal places if necessary.

Easy
2min
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Outcomes

2.2.8

establish and use the formula S_n=t_1 (r^n−1)/(r−1) for the sum of the first n terms of a geometric sequence

2.2.9

use geometric sequences in contexts involving geometric growth or decay, such as compound interest

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