Answer:
f(3) = 1.432
Explanation:
You want to know the third term of the sequence defined by ...
- f(1) = 0.2
- f(n) = (2/5)f(n-1) +1
Sequence
The terms of the sequence can be found one at a time by evaluating the recursive relation. The attached calculator output shows the first three terms are ...
f(1) = 0.2 . . . . . . . given
f(2) = 0.4(0.2) +1 = 1.08
f(3) = 0.4(1.08) +1 = 1.432
The third term of the sequence is 1.432.
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Additional comment
The explicit form of the function is ...
f(n) = 5/3 -11/3(2/5)^n
Terms will asymptotically approach a value of 5/3.
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