How to 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. Image titled Find a Number of Terms in an Arithmetic Sequence Step 1
    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. Image titled Find a Number of Terms in an Arithmetic Sequence Step 2
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    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. Image titled Find a Number of Terms in an Arithmetic Sequence Step 3
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    Calculate 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 difference between the last term, divide the first term by the common difference and add 1 to the quotient.

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.

Article Info

Categories: Algebra