Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. Arithmetic Sequences
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Exercise 48 Page 576

Does the difference between any two consecutive terms always have the same value?

Recursive Rule: for
Explicit Rule: for

Practice makes perfect
Let's pay close attention to the difference between two consecutive terms.
We can see that the difference between any two consecutive terms is

Recursive Rule

Let's now consider the general formula for a recursive rule.
In the above formula, is the first term of the sequence and is the common difference. For our sequence, the first term is and the common difference is

Explicit Rule

Finally, let's recall the general formula for an explicit rule.
Again, represents the first term of the sequence and is the common difference. As we have already stated, for our sequence, we have and