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What is the common difference of the arithmetic sequence 5 8 11?

Published in Arithmetic Sequences 1 min read

The common difference of the arithmetic sequence 5, 8, 11 is 3.

Understanding Common Difference in Arithmetic Sequences

The common difference is the constant value that is added to each term in an arithmetic sequence to get the next term. According to the provided reference, we can calculate it by subtracting any term from the term that follows it.

Calculating the Common Difference

In the arithmetic sequence 5, 8, 11:

  • The difference between the second term (8) and the first term (5) is 8 - 5 = 3.
  • The difference between the third term (11) and the second term (8) is 11 - 8 = 3.

Since the difference between consecutive terms is constant, the common difference is indeed 3.

Example

As an additional example from the reference, if we wanted to find the 10th term we can use the following formula:

an = a1 + (n-1) * d

Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

So, for the 10th term:

a10 = 5 + (10-1) 3 = 5 + 9 3 = 5 + 27 = 32