Finding the number of terms in an arithmetic sequence might sound like a complex task, but it’s actually pretty straightforward. All you need to do is plug the given values into the formula tn = a + (n - 1) d and solve for n, which is the number of terms. Note that tn is the last number in the sequence, a is the first term in the sequence, and d is the common difference.

Steps

  1. 1
    Identify the first, second, and last terms of the sequence. Typically, to solve a problem like this, you’ll be given the first 3 or more terms as well as the last term.[1]
    • For example, you may have the following sequence: 107, 101, 95…-61. In this case, the first term is 107, the second term is 101, and the last term is -61. You need all of this information to solve the problem.
  2. 2
    Subtract the first term from the second term to find the common difference. In the example sequence, the first term is 107 and the second term is 101. So, subtract 107 from 101, which is -6. Therefore, the common difference is -6.[2]
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  3. 3
    Use the formula tn = a + (n - 1) d to solve for n. Plug in the last term (tn), the first term (a), and the common difference (d).[3] Work through the equation until you’ve solved for n.[4]
    • For example, start by writing: -61 = 107 + (n - 1) -6. Subtract 107 from both sides so you’re left with -168 = (n - 1) -6. Then, divide both sides by -6 to get 28 = n - 1. Finish by adding 1 to both sides so that n = 29.
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Community Q&A

  • Question
    Can I use the formula (A - L/d) + 1 for finding n?
    Donagan
    Donagan
    Top Answerer
    As explained above, n = [(L - A) / d] + 1.
  • Question
    If the difference is not given, how do I find the difference?
    Donagan
    Donagan
    Top Answerer
    Subtract any term from the one that follows it.
  • Question
    If the first term and last term of an arithmetic progression are 5 and 89, how do I find the number of terms?
    Donagan
    Donagan
    Top Answerer
    You can't without knowing the difference between consecutive terms.
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Warnings

  • Do not confuse the difference between the first and last term with the common difference.
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About This Article

Sophia Latorre
Co-authored by:
wikiHow Staff Writer
This article was co-authored by wikiHow staff writer, Sophia Latorre. Sophia Latorre is a Content Manager on the wikiHow team. Before joining wikiHow, Sophia worked as a technical editor and was published in six International Energy Agency (IEA) Wind Annual Reports. Now, she writes, edits, and reviews articles for the wikiHow Content Team, working to make the content as helpful as possible for readers worldwide. Sophia holds a BA in English from Colorado State University. This article has been viewed 439,650 times.
111 votes - 71%
Co-authors: 12
Updated: August 29, 2022
Views: 439,650
Categories: Algebra
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