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3.05 Geometric sequences with technology

Interactive practice questions

Consider the following recursive definition.

$T_{n+1}=0.2T_n$Tn+1=0.2Tn, $T_1=25$T1=25

State the first $4$4 terms in the sequence.

Enter each term on the same line, separated by commas.

Easy
< 1min

Consider the following recursive definition which starts from $T_1$T1.

$T_n=\frac{1}{4}T_{n-1}$Tn=14Tn1, $T_5=\frac{1}{4}$T5=14

Easy
1min

Consider the first four terms in the following geometric sequence.

Easy
2min

Consider the sequence defined by $a_1=2$a1=2 and $a_n=3a_{n-1}$an=3an1 for $n\ge2$n2.

Easy
1min
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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 𝑛𝑡ℎ term using 𝑡_𝑛 = 𝑎r^(𝑛−1) where 𝑡_𝑛 represents the 𝑛th term of the sequence, 𝑎=first term, 𝑛=term number and 𝑟=common ratio of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions

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