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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

ACMGM071

use recursion to generate a geometric sequence

ACMGM072

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

ACMGM073

deduce a rule for the nth term 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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