How to Find the Number of Terms in an Arithmetic Series: 3 Steps

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How to Find the Number of Terms in an Arithmetic Series: 3 Steps
How to Find the Number of Terms in an Arithmetic Series: 3 Steps

Video: How to Find the Number of Terms in an Arithmetic Series: 3 Steps

Video: How to Find the Number of Terms in an Arithmetic Series: 3 Steps
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Finding the number of terms in an arithmetic series may sound daunting, but it's actually quite simple. You just need to enter the numbers into the formula U = a + (n - 1) b and find the value of n, which is the number of terms. Know that U is the last number in the series, a is the first term in the series, and b is the difference or difference between adjacent terms.

Step

Find a Number of Terms in an Arithmetic Sequence Step 1
Find a Number of Terms in an Arithmetic Sequence Step 1

Step 1. Identify the first, second, and last terms in the series

Usually, questions like this give the first 3 or more terms, and the last term.

For example, your question looks like this: 107, 101, 95…-61. In this case, the first term is 107 and the last term is -61. You need all this information to solve the problem

Find a Number of Terms in an Arithmetic Sequence Step 2
Find a Number of Terms in an Arithmetic Sequence Step 2

Step 2. Subtract the second term from the first term to find the difference (b)

In the example problem, the first term is 107 and the second term is 101. To find the difference, subtract 101 by 107 and get -6.

Find a Number of Terms in an Arithmetic Sequence Step 3
Find a Number of Terms in an Arithmetic Sequence Step 3

Step 3. Use the formula U = a + (n - 1) b to find n.

Enter the last term (U ), the first term (a), and the difference (b). Count the equations until you get the value of n.

For our example problem, write: -61 = 107 + (n - 1) -6. Subtract 107 from both sides so that only -168 = (n - 1) -6 remains. Then, divide both sides by -6 to get 28 = n - 1. Solve by adding 1 to both sides so n = 29

Tips

The difference between the first and last terms will always be divisible by difference

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