Is the Sequence Arithmetic? Yes. Explanation: See solution. Recursive Formula:A(n)=A(n−1)−4,A(1)=-3 Explicit Formula:A(n)=-3+(n−1)(-4)
Practice makes perfect
When a sequence is arithmetic, the difference between two consecutive terms is constant. Examining our sequence we can see that this is the case.
-3⟶+(-4)-7⟶+(-4)-11⟶+(-4)-15⟶+(-4)…
Since the difference between consecutive terms is constant and equal to -4, we have an arithmetic sequence with common difference-4. We will use this information to write both the recursive and the explicit formula.
Recursive Formula
Let's recall the general form of the recursive formula for an arithmetic sequence.
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