Periodic Sequences - Definition & Examples
Read this topicExplanations 3
- Periodic sequences Periodic sequences continually repeat themselves every ppp terms. A periodic sequence can be thought of as the discrete version of a periodic function. In par…
By Daniel Liu, Ruiran Xun, Victor Wang, Caroline K, Anusha Rahman
- What is a periodic sequence? A period sequence is a sequence with a repeating pattern of terms. The following sequences are all periodic: 0,1,0,1,0,1,...0, 1, 0, 1, 0, 1, ...0,1…
By Liza Sulkin, Jonathan Heller, Anusha Rahman
- (Video) Periodic Sequences by Anusha Rahman In this video, Anusha Rahman goes over how to determine whether a string of numbers is a periodic sequence, how to find the period, a…
By Anusha Rahman
Problems 22
- Is 1,2,3,2,3,4,1,2,3,2,3,4,...1,2,3,2,3,4,1,2,3,2,3,4,...1,2,3,2,3,4,1,2,3,2,3,4,... (continuing with the same pattern) a periodic sequence?
- What is the smallest period of 1,2,3,1,2,3,1,2,3{1,2,3,1,2,3,1,2,3}1,2,3,1,2,3,1,2,3?
- Which formula describes the periodic sequence a=−2,2,−2,2,−2,2,…,a = -2,2,-2,2,-2,2,\dots,a=−2,2,−2,2,−2,2,…, using n=1n=1n=1 for the first term?
- Is 1,8,9,10,2,3,...{1,8,9,10,2,3,...}1,8,9,10,2,3,... a periodic sequence if the next members of the sequence are random?
- Is 1,−2,3,−4,5,−6,7,−8,...{1, -2, 3, -4, 5, -6,7,-8,...}1,−2,3,−4,5,−6,7,−8,... a periodic sequence if every one of the next terms is ramdom?
- Is 1,2,−3,4,5,−6,7,8,−9,...{1, 2, -3, 4, 5, -6,7, 8, -9, ...}1,2,−3,4,5,−6,7,8,−9,... a periodic sequence if the next terms are random?
- Is 1,−2,2,−1,1,−2,2,−1,1,−2,2,−1,...1, -2, 2, -1, 1, -2, 2, -1, 1, -2, 2, -1,...1,−2,2,−1,1,−2,2,−1,1,−2,2,−1,... (continuing with the same pattern) a periodic sequence?
- Is 1,2,3,4,5,6,....1,2,3,4,5,6,....1,2,3,4,5,6,.... (continuing with the same pattern) a periodic sequence?
- Is this a periodic sequence? 1,2,3,1,2,3,1,2,3,1,...{1, 2, 3, 1, 2, 3, 1, 2, 3, 1, ... }1,2,3,1,2,3,1,2,3,1,...
- True or False\text{True or False}True or False 4,1,2,3,3,9,9,3,2,8...4, 1, 2, 3, 3, 9, 9, 3, 2, 8...4,1,2,3,3,9,9,3,2,8... must be a periodic sequence.
- Is this a periodic sequence? 1,−1,1,−1,−1,1,…1, -1, 1, -1, -1, 1, \dots1,−1,1,−1,−1,1,…
- Find the hidden periodic sequence in 157\frac{15}{7}715. What is the period?
- Is it periodic? What is the period?
- We have periodic sequence: 1,3,5,7,9,1,3,5,7,9,...1,3,5,7,9,1,3,5,7,9,...1,3,5,7,9,1,3,5,7,9,... What is the 36th36^\text{th}36th element?
- We have periodic sequence: 3,2,4,3,5,4,3,2,4,3,5,4...3,2,4,3,5,4,3,2,4,3,5,4...3,2,4,3,5,4,3,2,4,3,5,4... What is the period of this sequence?
- We have a periodic sequence: 3,2,4,3,5,4,3,2,4,3,5,4...3,2,4,3,5,4,3,2,4,3,5,4...3,2,4,3,5,4,3,2,4,3,5,4... What is the 123rd123^\text{rd}123rd element of this sequence?
- Can all repeating decimals be converted into a fraction?
- Take a look at the yyy-values of the function above. Are they periodic?
- 1,11,21,1211,111221,312211...1,11,21,1211,111221,312211...1,11,21,1211,111221,312211... Is the sequence above periodic, if it follows the same pattern?
- True or False\text{True or False}True or False === Are the digits in the decimal expansion π=3.14…\pi = 3.14\dotsπ=3.14… periodic?
- Define a sequence {an}\{a_n\}{an} by a1=2017,a2=2018a_1=2017, a_2 = 2018a1=2017,a2=2018 and an=an−1−an−2.a_n = a_{n-1}-a_{n-2}.an=an−1−an−2. What is the value of a1+a2+a3+…
- Define a sequence {xn}\{x_n\}{xn} for positive integers nnn such that x1=57,x2=68,x3=32x_1=57, x_2 = 68, x_3=32x1=57,x2=68,x3=32 and xn=xn−1−xn−2+xn−3x_n = x_{n-1}-x_{n-2} +…