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3.03 Arithmetic Sequences with technology

Interactive practice questions

Consider the sequence defined by $a_1=6$a1=6 and $a_n=a_{n-1}+5$an=an1+5 for $n\ge2$n2.

a

What is the $21$21st term of the sequence?

b

What is the $22$22nd term of the sequence?

c

What is the $23$23rd term of the sequence?

d

What is the $24$24th term of the sequence?

e

What is the $25$25th term of the sequence?

Easy
2min

Consider the first-order recurrence relationship defined by $T_n=T_{n-1}+2$Tn=Tn1+2, $T_1=5$T1=5.

Easy
2min

Consider the first-order recurrence relationship defined by $T_n=T_{n-1}-2$Tn=Tn12, $T_1=5$T1=5.

Easy
2min

Consider the sequence plot drawn below.

Easy
2min
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Outcomes

3.3.1.1

use recursion to generate an arithmetic sequence

3.3.1.2

display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations

3.3.1.3

use the rule for the 𝑛𝑡ℎ term using 𝑡_𝑛 = 𝑎+(𝑛–1)𝑑, where 𝑡_𝑛 represents the 𝑛𝑡ℎ term of the sequence, 𝑎= first term, 𝑛=term number and 𝑑=common difference of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions

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