Topics
3. Growth & Decay in Sequences
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AustraliaQLD
Year 12

3.04 Geometric sequences

Lesson
Worksheet
Practice

Interactive practice questions

Study the pattern for the following geometric sequence, and write down the next two terms.

$3$3, $15$15, $75$75, $\editable{}$, $\editable{}$

Easy
< 1min

Find the next three terms of the sequence.

Easy
< 1min

Study the pattern for the following geometric sequence, and write down the next two terms.

Easy
< 1min

Study the pattern for the following geometric sequence, and write down the next two terms.

Easy
2min
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Outcomes

3.3.2.1

use recursion to generate a geometric sequence

3.3.2.2

display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations

3.3.2.3

use the rule for the π‘›π‘‘β„Ž term using 𝑑_𝑛 = π‘Žr^(π‘›βˆ’1) where 𝑑_𝑛 represents the 𝑛th term of the sequence, π‘Ž=first term, 𝑛=term number and π‘Ÿ=common ratio of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions

3.3.2.4

use geometric sequences to model and analyse (numerically or graphically only) practical problems involving geometric growth and decay (logarithmic solutions not required), such as analysing a compound interest loan or investment, the growth of a bacterial population that doubles in size each hour or the decreasing height of the bounce of a ball at each bounce; or calculating the value of office furniture at the end of each year using the declining (reducing) balance method to depreciate

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