Does the difference between any two consecutive terms always have the same value?
Recursive Rule: f(1)=-4, f(n)=f(n-1)-4, for n≥ 2 Explicit Rule: f(n)=- 4-4(n-1), for n≥ 1
Practice makes perfect
We want 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.
-4 - 4 → -8 - 4 → -12 - 4 → -16 - 4 → -20...
We can see that the difference between any two consecutive terms is -4.
Recursive Rule
Let's now consider the general formula for a recursive rule.
&f(1)=a
&f(n)=f(n-1)+d,forn≥ 2
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 -4 and the common difference is -4.
&f(1)= -4
&f(n)=f(n-1) -4,forn≥ 2
Explicit Rule
Finally, let's recall the general formula for an explicit rule.
f(n)=a+d(n-1),forn≥ 1
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= -4 and d= -4.
f(n)= - 4 -4(n-1),forn≥ 1
