Does the difference between any two consecutive terms always have the same value?
Recursive Rule:f(1)=0,f(n)=f(n−1)+81, for n≥2 Explicit Rule:f(n)=0+81(n−1), for n≥1
Practice makes perfect
Let's pay close attention to the difference between two consecutive terms.
0→+8181→+8141→+8183…
We can see that the difference between any two consecutive terms is 81.
Recursive Rule
Let's now consider the general formula for a recursive rule.
f(1)=af(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 0 and the common difference is 81.
f(1)=0f(n)=f(n−1)+81,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=0 and d=81.
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