standard_description: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
problem_activity: Problem 1
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.
[IMG]
b.
[IMG]
c.
[IMG]
Problem 2
An arithmetic sequence is shown below.
$${29,\space 22,\space15,\space8,\space1,\space…}$$
Write a recursive formula to represent the sequence.
Write an explicit formula to represent the sequence.
Find the 10th term in the sequence.
Find the 100th term in the sequence.
Problem 3
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.
$${a_{n+1}=a_n-{3\over2}}$$
,
$${a_1=10}$$


aligns: yes