David W. answered • 11/16/15
Tutor
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Experienced Prof
The sequence has a starting value -- f(1)=2.
Then, there are more values, like f(2)=5 and so on.
Now, to go from 2 to 5 allows many possibilities for a "rule," so more values are given. First, look for a "common difference" between the values. Each value given is 3 more than the current value. That rule looks like this:
f(n) = f(n-1) + 3 with f(1)=2
When there is a common difference (the constant value d), we have a rule for an Arithmetic Sequence.
f(n) = f(n-1) + d with f(1)=2 and d=3
Then, there are more values, like f(2)=5 and so on.
Now, to go from 2 to 5 allows many possibilities for a "rule," so more values are given. First, look for a "common difference" between the values. Each value given is 3 more than the current value. That rule looks like this:
f(n) = f(n-1) + 3 with f(1)=2
When there is a common difference (the constant value d), we have a rule for an Arithmetic Sequence.
f(n) = f(n-1) + d with f(1)=2 and d=3
The term f(n) = a + (n-1)d where a=f(1)
so, f(n) = 2 + (n-1)(3)
To find f(100):
f(100) = 2 + (100-1)(3)
f(100) = 2 + 297
f(100) = 299
