How to Find a Number of Terms in Arithmetic Sequence


Equal intervals, called the common difference, separate the terms of an arithmetic sequence. The common difference can be either a positive or a negative number. For example, [2, 5, 8, 11...] is an arithmetic sequence with a common difference of 3, while [2, -1, -4, -7...] is an arithmetic sequence with a common difference of -3. In order to find a term in an arithmetic sequence, you need a starting point and the common difference. The general definition of the arithmetic sequence is a(n) = a(1) + (n - 1)d.

Things You'll Need

  • Calculator (optional)
  • Define the starting point. This is critical because all the terms you find have to be referenced to the same starting point. This will either be a part of the problem statement or you will have to choose it. Put the starting value in the arithmetic sequence equation.

    a(1) = 3

    a(n) = 3 + (n - 1)d

  • Define the common difference. Like the starting point, this will either be part of the problem or you will have to choose it. Put it into the equation.

    d = 5

    a(n) = 3 + (n - 1)5

  • Decide which terms you want to calculate. These will be the values for "n" in the equation. For this example, use n = [3, 7, 9, 11] for the third, seventh, ninth, and eleventh terms.

  • Calculate the value in the arithmetic sequence for each value of n.

    a(3) = 3 + (3 - 1)5 =13
    a(7) = 3 + (7 - 1)5 = 33
    a(9) = 3 + (9 - 1)5 = 43
    a(11) = 3 + (11 - 1)5 = 53

  • Check your work, if practical, by writing out the series to include all of your values for "n." This will not be practical for very high values of n but it can increase confidence when using lower values of n.

    a(n) = 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58

    The third, seventh, ninth, and eleventh terms in this sequence match the calculations from the previous step.


Promoted By Zergnet


You May Also Like

  • How to Calculate Series

    When you need to add up a set of numbers in a pattern, whether it's geometric or arithmetic in nature, you can...

  • How to Find Arithmetic Mean

    Finding an arithmetic mean doesn't have to mean confusion and frustration. The arithmetic mean is another term for the average of numbers....

  • How to Calculate the Sum of a Geometric Series

    A geometric series is a sequence of numbers created by multiplying each term by a fixed number to get the next term....

  • How to Find the Geometric Sequence

    In a geometric sequence, each number in a series of numbers is produced by multiplying the previous value by a fixed factor....

  • How to Find Fraction Sequences

    Algebra class will frequently require you to work with sequences, which can be arithmetic or geometric. Arithmetic sequences will involve obtaining a...

  • How to Find the Nth Term in Cubic Sequences

    After you have learned to solve problems with arithmetic and quadratic sequences, you may be asked to solve problems with cubic sequences....

  • How to Find the Nth Term & Function Rule

    A sequence is an ordered list of numbers that is defined by a rule or a function. Each number in the sequence...

  • Solving Math Sequences

    There are two kinds of math sequences that can be solved: arithmetic sequences and geometric sequences. An arithmetic sequence is solved by...

Related Searches

Check It Out

Can You Take Advantage Of Student Loan Forgiveness?

Is DIY in your DNA? Become part of our maker community.
Submit Your Work!