Write explicit rules for arithmetic sequences and translate between explicit and recursive formulas.
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The formula for an explicit rule for an arithmetic sequence is given by $${a_n=a_1+d(n-1)}$$, where $$d$$ is the common difference and $$n$$ is the term number.
Write an explicit rule for the number of tiles in each pattern shown below.
a.
b.
c.
An arithmetic sequence is shown below.
$${29,\space 22,\space15,\space8,\space1,\space…}$$
An arithmetic sequence is described by either a recursive or explicit rule below. If given a recursive rule, provide the explicit rule. If given the explicit rule, give the recursive rule.
a. $${f(n)=6(n-1)+1}$$, for $${n\geq1}$$
b. $${a_{n+1}=a_n-{3\over2}}$$, $${a_1=10}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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An arithmetic sequence and its recursive formula are shown below.
Sequence: $${2,11,20,29,38,…}$$
Recursive formula: $${a_{n+1}=a_n+9}$$, where $${a_n=2}$$
Your teacher asks you to find the 100th term in the sequence. Max, a student in your class, says that he plans to use the recursive formula to determine the 100th term.