Arithmetic Sequences

Key Questions

  • What is an arithmetic sequence?

    An arithmetic sequence is a sequence (list of numbers) that has a common difference (a positive or negative constant) between the consecutive terms.

    Here are some examples of arithmetic sequences:
    1.)7, 14, 21, 28 because Common difference is 7.
    2.) 48, 45, 42, 39 because it has a common difference of - 3.

    The following are not examples of arithmetic sequences:

    1.) 2,4,8,16 is not because the difference between first and second term is 2, but the difference between second and third term is 4, and the difference between third and fourth term is 8. No common difference so it is not an arithmetic sequence.

    2.) 1, 4, 9, 16 is not because difference between first and second is 3, difference between second and third is 5, difference between third and fourth is 7. No common difference so it is not an arithmetic sequence.

    3.) 2, 5, 7, 12 in not because difference between first and second is 3, difference between second and third is 2, difference between third and fourth is 5. No common difference so it is not an arithmetic sequence.

    Elizabeth P. · 3 · Sep 29 2014
  • How do I find the nth term of an arithmetic sequence?

    Answer:

    a_n=a_1+(n-1)*d
    color(white)("XXX")where a_1 is the first term and
    color(white)("XXXXXXX")d is the difference between a term and its previous term.

    Explanation:

    Examine the pattern:

    a_1
    a_color(brown)(2)=a_1+d=color(green)(a_1+1d)
    a_color(brown)(3)=a_2+d=a_1+d+d=color(green)(a_1+2d)
    a_color(brown)(4)=a_3+d=a_1+2d+dcolor(green)(=a_1+3d)
    a_color(brown)(5)=a_4+d=a_1+3d+d=color(green)(a_1+4d)

    Alan P. · 1 · Mar 25 2016
  • How do I find the common difference of an arithmetic sequence?

    Answer:

    To find out the common difference in an AP you can perform the following simple step.

    Explanation:

    Subtract the first term of the AP from the second term of the AP.

    d = a_2 - a_1

    where d = common difference
    a_2 = any term other than first term
    a_1 = previous term

    For example;

    In the AP
    3 , 9 , 15 , 21 , 27 , 33

    Taking a_1 = 3
    Taking a_2 = 9

    a_2 - a_1 = 9 - 3 = 6

    hence , common difference or d = 6

    Thanks

    I hope this helps

    yash · 8 · Jun 22 2017
  • What is an example of an arithmetic sequence?

    Answer:

    The even numbers, the odd numbers, etc

    Explanation:

    An arithmetic sequence is builded up adding a constant number (called difference) following this method

    a_1 is the first element of a arithmetic sequence, a_2 will be by definition a_2=a_1+d, a_3=a_2+d, and so on

    Example1:

    2,4,6,8,10,12,....is an arithmetic sequence because there is a constant difference between two consecutive elements (in this case 2)

    Example 2:

    3,13,23,33,43,53,.... is an arithmetic sequence because there is a constant difference between two consecutive elements (in this case 10)

    Example 3:

    1,-2,-5,-8,... is another arithmetic sequence with difference -3

    Hope this help

    F. Javier B. · 3 · Mar 8 2018

Questions

Sequences