Find a Number of Terms in an Arithmetic Sequence

Sometimes we come across problems in mathematics where we need to find out the number of terms in an arithmetic progression. It's not an uphill task and the number of terms can be found out in the following manner.

Steps

1. Find out the common difference. It will either be given directly in the problem, or two consecutive terms will be given from either the start or the end of the arithmetic progression. Let the common difference be denoted by d.
2. Identify the first and last term of the sequence. First term and last term are required to find out the number of terms of an Arithmetic Progression. Identify them and note them down. Let the first term be represented by A and let the last term be represented by L.
3. Calculate the number of terms by using the following formula: Let the number of terms be represented by n. The formula is:

   n = (L-A)/d + 1

   The formula is very simple. Divide the common difference (d) into the difference between the last term (L) and the first term (A), and then add 1.

Tips

• The difference between the last term and first term will always be divisible by the common difference.

Warnings

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

Related Articles

• Find Any Term of an Arithmetic Sequence
• Find the Sum of an Arithmetic Sequence

See also

• Use the Slope Intercept Form (in Algebra)
• Start Working with Continued Fractions
• Convert a Quadratic Formula to Roots Form by Completing the Square
• Factor Second Degree Polynomials (Quadratic Equations)
• Understand Linear Equations
• Understand Slope (in Algebra)
• Prove That the Square Root of Two Is Irrational
• Factor a Cubic Polynomial
• Calculate Frequency
• Find the Maximum or Minimum Value of a Quadratic Function Easily

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What links here

• Find the Sum of an Arithmetic Sequence