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• Arithmetic sequence
  ...ms is constant. This constant is called the '''common difference''' of the sequence. ...difference <math>1</math> and <math>99, 91, 83, 75</math> is an arithmetic sequence with common difference <math>-8</math>; however, <math>7, 0, 7, 14</math> a
  4 KB (736 words) - 02:00, 7 March 2024
• Arithmetic Sequence
  #REDIRECT[[Arithmetic sequence]]
  32 bytes (3 words) - 17:05, 3 September 2021

Page text matches

• 2016 AMC 10A Problems/Problem 10
  ..., 2x+14</math> is an arithmetic progression, meaning that the terms in the sequence increase by the same amount each term.
  2 KB (337 words) - 14:56, 25 June 2023
• Euler's Totient Theorem
  ...MC 10B]]) Let <math>a_1,a_2,\dots,a_{2018}</math> be a strictly increasing sequence of positive integers such that <cmath>a_1+a_2+\cdots+a_{2018}=2018^{2018}.<
  3 KB (542 words) - 17:45, 21 March 2023
• Algebra/Intermediate
  * [[Sequence | Sequences]] and [[Series]] ** [[Arithmetic sequence]]
  2 KB (198 words) - 17:47, 3 November 2021
• Prime number
  3,5 and 7 are the only primes that form an [[Arithmetic sequence]] with common difference 2. 3,7 and 11 are the only primes that form an [[Arithmetic sequence]] with common difference 4.
  6 KB (985 words) - 12:38, 25 February 2024
• Muirhead's Inequality
  ...y''' states that if a sequence <math>p</math> [[Majorization|majorizes]] a sequence <math>q</math>, then given a set of positive reals <math>x_1,x_2,\cdots,x_n The inequality is easier to understand given an example. Since the sequence <math>(5,1)</math> majorizes <math>(4,2)</math> (as <math>5>4, 5+1=4+2</mat
  8 KB (1,346 words) - 12:53, 8 October 2023
• Logarithm
  * The [[sequence]] <math> a_1, a_2, \ldots </math> is [[geometric sequence|geometric]] with <math> a_1=a </math> and common [[ratio]] <math> r, </math
  4 KB (680 words) - 12:54, 16 October 2023
• Sequence
  A '''sequence''' is an ordered list of terms. Sequences may be either [[finite]] or [[in ...th>f(x) = x^2</math> defined on <math>\mathbb{N}</math> corresponds to the sequence <math>X = (x_n) = (0, 1, 4, 9, 16, \ldots)</math>.
  2 KB (413 words) - 21:18, 13 November 2022
• Geometric sequence
  ...e terms is constant. This constant is called the '''common ratio''' of the sequence. ...n ratio <math>2</math> and <math>100, -50, 25, -25/2</math> is a geometric sequence with common ratio <math>-1/2</math>; however, <math>1, 3, 9, -27</math> and
  4 KB (644 words) - 12:55, 7 March 2022
• Arithmetic sequence
  ...ms is constant. This constant is called the '''common difference''' of the sequence. ...difference <math>1</math> and <math>99, 91, 83, 75</math> is an arithmetic sequence with common difference <math>-8</math>; however, <math>7, 0, 7, 14</math> a
  4 KB (736 words) - 02:00, 7 March 2024
• Geometry
  ...s length, width, and position. It is two-dimensional. The point/line/plane sequence can be extended to spaces and higher dimensions.
  3 KB (393 words) - 07:59, 25 September 2020
• Limit
  ...h> has a limit <math>L = \lim_{x \rightarrow c} f(x)</math> if for every [[sequence]] <math>\left\langle x_n \right\rangle</math> that converges to <math>c</ma
  7 KB (1,325 words) - 13:51, 1 June 2015
• 2006 AIME I Problems/Problem 15
  Given that a sequence satisfies <math> x_0=0 </math> and <math> |x_k|=|x_{k-1}+3| </math> for all ..._{k + 1}|\pm3 = |x_k|\pm3\mp3 = |x_k| = |x_{k - 1} + 3|</math>. So the new sequence works under the same criteria as the old one. In this way, we can pair all
  6 KB (910 words) - 19:31, 24 October 2023
• 2021 JMC 10
  ...bers <cmath>24_b,n,57_b,72_b, \ldots</cmath> form an increasing arithmetic sequence in that specific order. Then, what is the value of <math>n,</math> expresse ...1</math> for positive integers <math>n \ge1.</math> How many terms of this sequence are divisible by <math>99?</math>
  12 KB (1,784 words) - 16:49, 1 April 2021
• 2005 AMC 12A Problems
  arithmetic sequence, although not necessarily in that order. What is the middle term of the arithmetic sequence?
  13 KB (1,971 words) - 13:03, 19 February 2020
• 2004 AMC 12A Problems
  A sequence of three real numbers forms an arithmetic progression with a first term of
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2000 AMC 12 Problems
  ...s is the last to appear in the units position of a number in the Fibonacci sequence?
  13 KB (1,948 words) - 12:26, 1 April 2022
• 2002 AMC 12B Problems
  .../math> and <math>v, w, x, y, </math> and <math>z</math> form an arithmetic sequence. Find the value of <math>x</math>. ...an increasing arithmetic sequence and <math>a,b,d</math> form a geometric sequence, then <math>\frac ad</math> is
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2004 AMC 12B Problems
  In the sequence <math>2001</math>, <math>2002</math>, <math>2003</math>, <math>\ldots</math <math>2004^\textrm{th}</math> term in this sequence?
  13 KB (2,049 words) - 13:03, 19 February 2020
• Set
  .... If <math>AB, BC, CD, DE,</math> and <math>EA</math> form an [[arithmetic sequence]] (not necessarily in increasing order), find the value of <math>CD</math>.
  11 KB (2,021 words) - 00:00, 17 July 2011
• 1991 AJHSME Problems
  ...lying on a table, the paper is folded in half four times in the following sequence:
  17 KB (2,246 words) - 13:37, 19 February 2020

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