Does the difference between any two consecutive terms always have the same value?
See solution.
Practice makes perfect
We want to write the recursive rule and the explicit rule for the given arithmetic sequence. Let's pay close attention to the difference between two consecutive terms.
5 -2 ⟶ 3 -2 ⟶ 1 -2 ⟶ -1 ...
We can see that the difference between any two consecutive terms is -2.
Recursive Rule
Let's now consider the general formula for a recursive rule.
&A(1)=a
&A(n)=A(n-1)+d
In the above formula, a is the first term of the sequence and d is the common difference.
For our sequence, the first term is 5 and the common difference is -2.
&A(1)= 5
&A(n)=A(n-1) - 2
Explicit Rule
Finally, let's recall the general formula for an explicit rule.
A(n)=a+(n-1)d
Again, a represents the first term of the sequence and d is the common difference. As we have already stated, for our sequence, we have a= 5 and d= -2.
A(n)= 5+(n-1)( -2)
