Transcript sequences-day 1 (2) File

Announcements
Short Unit
• Today – constructing arithmetic sequences
• Arithmetic sequences WS due Tuesday
• Monday – modeling with sequences
• Tuesday – performance task (summative)
What we’re learning today:
• Given an explicit rule (function) for a sequence, how to find number
in the sequence.
• Given a sequence of numbers, how to find the explicit rule.
A go-kart racing track charges $5 for a go-kart license and $2 for each lap. If you list the charges for 1
lap, 2 laps, 3 laps, and so on, in order, the list forms a sequence of numbers:
• 7, 9, 11, 13,…
• Common difference: the difference between two consecutive
terms
• Arithmetic sequence: A sequence that has a common
difference
Explicit Rule
An explicit rule for a sequence defines the nth term as a function of n for any
whole number n greater than 0. Explicit rules can be used to find any specific
term in a sequence without finding any of the previous terms.
For the previous problem, the explicit rule is:
7, 9, 11, 13,…
f(n) = 2n + 5
Use the explicit rule to find the 15th, 16th, and 17th numbers in the sequence
Explore: Write an explicit rule for each sequence:
1.
2.
3. Lucia knows the fourth term in a sequence is 55 and the ninth term in the
same sequence is 90. Explain how she can find the common difference for the
sequence. Then find the second term of the sequence.
4. Challenge: Write an explicit rule for the following sequence (hint:
everything we just learned about how to write explicit rules won’t work
here because this isn’t an arithmetic sequence, so you will have to be
creative).
1 2 3 4
, , , ,…
Write the explicit rule for the sequence
• 2,
5
,
2
3,
7
,….
2
Write:
• How do you write the explicit rule for the sequence 18, 17, 16, …