Name:
Sequences!, Sequences, Sequence, Sequenc, Sequen, Seque, Sequ, Seq, Se, S
Set 1
Question 1
The diagram below represents the first three terms of a sequence.
Create an explicit formula for 𝑎𝑛 , the number of shaded squares in the 𝑛th term.
Question 2
Create an explicit formula for the sequence defined recursively as 𝑎1 = 6 and 𝑎𝑛 = 3𝑎𝑛−1
Question 3
A sunflower is 3 inches tall at week 1 and grows 2 inches each week. Which function(s) shown below can be
used to determine the height, 𝑓(𝑛), of the sunflower in 𝑛 weeks?
I. 𝑓(𝑛) = 2𝑛 + 3
II. 𝑓(𝑛) = 2(𝑛 − 1) + 3
III. 𝑓(𝑛) = 𝑓(𝑛 − 1) + 2 where 𝑓(0) = 1
Set 2
Question 1
1
Find the first four terms of the sequence defined recursively as 𝑎1 = 2 and 𝑎𝑛+1 = 1 − 𝑎𝑛
Question 2
If 𝑓(1) = 3 and 𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1, then find the value of 𝑓(5)
Question 3
In an arithmetic sequence, 𝑎4 = 19 and 𝑎7 = 31. Determine a formula for 𝑎𝑛 , the 𝑛th term in this sequence.
Set 3
Question 1
A function is recursively defined below:
𝑎1 = 𝑥 + 1
𝑎𝑛 = 𝑥(𝑎𝑛−1 )
Find the 10th term of this sequence
Question 2
In 2010, the population of New York State was approximately 19,378,000 with an annual growth rate of 1.5%.
Assuming the growth rate is maintained for a large number of years, create an explicit equation that can be used
to predict the population of New York State 𝑡 years after 2010.
Question 3
2𝑥
Find the fourth term of the sequence defined by 𝑎1 = 3𝑥𝑦 5 and 𝑎𝑛 = ( ) 𝑎𝑛−1
𝑦
Set 4
Question 1
Use the recursive sequence defined below to express the next three terms as fractions reduced to lowest terms
𝑎1 = 2
𝑎𝑛 = 3(𝑎𝑛−1 )−2
Question 2
The population of Jamesburg for the years 2010-2013 was reported as follows:
250,000
250,937
251,878
252,822
How should this sequence be modeled? In other words, should we use a linear or exponential function? Defend
your answer.
Question 3 (Big Challenge: Try This at Home!)
A sequence is defined as follows:
𝑎1 = 1
𝑎2 = 1 + 2 = 3
𝑎3 = 1 + 2 + 3 = 6
𝑎4 = 1 + 2 + 3 + 4 = 10
𝑎5 = 1 + 2 + 3 + 4 + 5 = 15
Find an explicit formula for 𝑎𝑛