Arithmetic Sequences - Definition & Examples
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- (Video) A Formula for the nthn^{\text{th}}nth Term by PatrickJMT This video by the PatrickJMT explains how to find the nth term of an arithmetic sequences. Summary\large{\text{S…
By Stefan Cuevas, Alex Federspiel, Liza Sulkin, Amy Feraco, Caroline K, Gabi Slizewska
- (Video) Arithmetic Progressions by Eddie Woo Here's some videos by Eddie Woo where he explains arithmetic sequences and series. Recall that a set is a collection of numbers, a s…
By Alex Federspiel, Liza Sulkin, Jonathan Heller, Anusha Rahman, Gabi Slizewska
- There are two main types of sequences we care about, because they have very noticeable patterns. But back up for a second, what IS a sequence? It's a collection of numbers writt…
By Joshua Siktar, Jonathan Heller, Gabi Slizewska
- Maximum Depth Exceeded: Fun with Sequences and Python, Part 2 To read part 1 of this story, go here. Our Python code lets us generate a sequence based on a recursive formula, wh…
By Joshua Siktar, Caroline K
Problems 22
- Find the common difference of the following arithmetic sequence: 1,3,5,7,9,11,… .1,3,5,7,9,11,\dots.1,3,5,7,9,11,….
- Find the explicit formula for the arithmetic sequence asasas beginning with 1,3,5,7,9,11,… .1,3,5,7,9,11,\dots.1,3,5,7,9,11,…. Let nnn represent the position of a term in the se…
- Find the common difference of the sequence 10,18,26,34,42,… .10,18,26,34,42,\dots.10,18,26,34,42,….
- Find the general term of the sequence 10,18,26,34,42,… .10,18,26,34,42,\dots.10,18,26,34,42,…. Let nnn represent the position of a term in the sequence, using n=1n=1n=1 for the …
- Find the 100th100^{\text{th}}100th term of the sequence 10,18,26,34,42,...10,18,26,34,42,...10,18,26,34,42,...
- The value 306306306 appears as the nnnth term of the arithmetic sequence 10,18,26,34,42,… .10,18,26,34,42,\dots.10,18,26,34,42,…. What is nnn?
- If an arithmetic sequence is described by the explicit formula an=18n−200a_{n} = 18n-200an=18n−200, find the value of a1+a2a_1 + a_2a1+a2.
- If an arithmetic sequence is described by the explicit formula an=1000n+20a_{n} = 1000n+20an=1000n+20, find the 30th30^{\text{th}}30th term of this sequence.
- You are given an arithmetic sequence ana_nan. If a9=28a_{9} = 28a9=28 and a20=50a_{20} = 50a20=50, find a1a_{1}a1.
- You are given an arithmetic sequence a1,a2,…,a100a_1,a_2,\dots,a_{100}a1,a2,…,a100. If a55=10a_{55} = 10a55=10 and a100=100a_{100} = 100a100=100, find a1a_{1}a1.
- Which of the following is an arithmetic sequence? Mark all that apply.
- What is the 50th50^{\text{th}}50th number in the following arithmetic sequence? 4,7,10,13,16,19,…4, 7, 10, 13, 16, 19, \dots4,7,10,13,16,19,…
- If the 4th4^{\text{th}}4th term of an arithmetic sequence is 666, and the 7th7^{\text{th}}7th term of the sequence is 888, find the 13th13^{\text{th}}13th term of the sequence.
- What is the common difference ddd for the following arithmetic sequence? 1,2,3,4,5,6,7,8,9,10,…1, 2, 3, 4, 5, 6, 7, 8, 9, 10,\dots1,2,3,4,5,6,7,8,9,10,…
- Find the common difference ddd for the arithmetic sequence 1,4,7,10,13,16,19,22,… .1, 4, 7, 10, 13, 16, 19, 22, \dots.1,4,7,10,13,16,19,22,….
- What is the common difference ddd for the following arithmetic sequence? 2,4,6,8,10,12,…2, 4, 6, 8, 10, 12, \dots2,4,6,8,10,12,…
- What is the common difference ddd for the following arithmetic sequence? 0,4,8,12,…0, 4, 8, 12,\dots0,4,8,12,…
- an=a1+(n−1)da_n=a_1+(n-1)dan=a1+(n−1)d What is the 4th4^{\text{th}}4th term in an arithmetic sequence with a common difference of d=5d = 5d=5? The first term of the sequence i…
- an=a1+(n−1)da_n=a_1+(n-1)dan=a1+(n−1)d What is the 101st101^{\text{st}}101st term in an arithmetic sequence with a common difference of d=10d = 10d=10? The first term of the s…
- You're on the Expii Titanic and wouldn't you know, it's sinking. But you don't want to give up the ship. Since it's sinking slowly you decide to measure the water level each hou…
- If a1,a2,a3,a4,…a10a_1, a_2, a_3, a_4, \ldots a_{10}a1,a2,a3,a4,…a10 is an arithmetic sequence which of the following are also arithmetic sequences?
- a,12,c,da,12,c,da,12,c,d is an arithmetic sequence with common difference xxx such that a,c,da,c,da,c,d is a geometric sequence. Given that xxx is not 000, what is the value of …