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  • *Division A: Series and Sequences **Regionals: Sequences (Arithmetic, Geometric, Other), explicit and recursive definitions
    8 KB (1,182 words) - 13:26, 3 April 2024
  • * [[Sequence | Sequences]] and [[Series]] ** [[Arithmetic sequence]]
    2 KB (198 words) - 15:06, 7 December 2024
  • A '''sequence''' is an ordered list of terms. Sequences may be either [[finite]] or [[infinite]]. ==Monotone Sequences==
    2 KB (413 words) - 20:18, 13 November 2022
  • ...1, 3, 9, -27</math> and <math>-3, 1, 5, 9, \ldots</math> are not geometric sequences, as the ratio between consecutive terms varies. ...= a_n / a_{n-1}</math>. A similar definition holds for infinite geometric sequences. It appears most frequently in its three-term form: namely, that constants
    4 KB (649 words) - 20:09, 19 July 2024
  • In [[algebra]], an '''arithmetic sequence''', sometimes called an '''arithmetic progression''', is a [[sequence]] of numbers such that the difference betwe ...0, 7, 14</math> and <math>4, 12, 36, 108, \ldots</math> are not arithmetic sequences, as the difference between consecutive terms varies.
    4 KB (736 words) - 01:00, 7 March 2024
  • ...ath> pairs of numbers each sum up to <math>-3</math>, and the rest form an arithmetic sequence, if the first <math>990</math> pairs sum up to <math>-3</math>, an The sums alternate between separate arithmetic sequences. One of them is of particular interest to us: specifically, the one that go
    8 KB (1,334 words) - 16:37, 15 December 2024
  • ...the first and last terms of <math>A</math>. This comes from the sum of an arithmetic sequence. ...ath>B</math>, and the difference between the greatest terms of the two two sequences is <math>99</math> (forget about absolute value, it's insignificant here si
    8 KB (1,431 words) - 16:50, 29 December 2024
  • ...ts77, </math> into which <math> + </math> signs are inserted to produce an arithmetic [[expression]]. For example, <math> 7+77+777+7+7=875 </math> could be obtai Let's write the sequences of <math>n</math>'s in a compact form , <math>T_p = 24 + 22 + 9(p-1)</math>
    11 KB (1,857 words) - 11:57, 18 July 2024
  • ...are shown below so that the numbers in each row and column form arithmetic sequences. Find the number that must occupy the vacant square marked by the asterisk
    6 KB (902 words) - 07:57, 19 June 2021
  • ...terms are formed by multiplying the corresponding terms of two arithmetic sequences.
    7 KB (1,127 words) - 08:02, 11 July 2023
  • ...are shown below so that the numbers in each row and column form arithmetic sequences. Find the number that must occupy the vacant square marked by the asterisk We begin with the table that was given to us and add in the following arithmetic progression on the bottom:
    5 KB (877 words) - 19:57, 27 December 2024
  • == Solution 3 (Finite Differences by Arithmetic) == Note that the second differences of all quadratic sequences must be constant (but nonzero). One example is the following sequence of pe
    9 KB (1,312 words) - 11:10, 15 December 2024
  • The [[average (Arithmetic)|average]] value of all such sums can be written in the form <math>\dfrac{p ...a_{10}</math>. We may do this because all sums obtained from these paired sequences are also obtained in another <math>2^5-1</math> ways by permuting the adjac
    5 KB (879 words) - 10:23, 5 September 2021
  • ...terms are formed by multiplying the corresponding terms of two arithmetic sequences. If you multiply the corresponding terms of two arithmetic sequences, you get the terms of a quadratic function. Thus, we have a quadratic <math
    5 KB (783 words) - 09:32, 3 February 2025
  • ...math>g_n</math> are the <math>n</math>th terms of arithmetic and geometric sequences, respectively. * [[Arithmetic sequence]]
    2 KB (477 words) - 18:39, 17 August 2020
  • ...of consecutive terms in a [[sequence]]. Common series are based on common sequences. * [[Arithmetic series]]
    400 bytes (43 words) - 20:21, 22 July 2021
  • ...<math>q</math> is <math>2</math> greater than <math>p</math>. What is the arithmetic mean of the two primes in the smallest twin prime pair? ...ath>m</math> and <math>n</math> is greater than <math>2007</math>, and the arithmetic mean of <math>m</math> and <math>n</math> is less than <math>2007</math>. H
    30 KB (4,794 words) - 22:00, 8 May 2024
  • The number of increasing sequences of positive integers <math>a_1 \le a_2 \le a_3 \le \cdots \le a_{10} \le 20 Let <math>x</math> be the arithmetic mean of all positive integers <math>k<577</math> such that <center><p><math
    6 KB (923 words) - 13:17, 16 January 2007
  • The numbers <math>3, 5, 7, a,</math> and <math>b</math> have an average (arithmetic mean) of <math>15</math>. What is the average of <math>a</math> and <math>b ...eflection across the <math>y</math>-axis. How many of the <math>125</math> sequences of three of these transformations (not necessarily distinct) will return <m
    13 KB (1,968 words) - 17:05, 23 November 2024
  • ...possible from 0 to 9, and then find all the possible permutations of these sequences. | Common difference || Sequences possible || Number of sequences
    2 KB (336 words) - 12:40, 31 December 2024

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