A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)? 52
2 answers:
Answer with Step-by-step explanation:
We are defined a sequence recursively as:
f(n + 1) = f(n) – 8
we are given f(1)=100
We have to find f(6)
f(2)=f(1)-8
f(3)=f(2)-8
=f(1)-8-8
= f(1)-16
f(4)=f(3)-8
=f(1)-16-8
=f(1)-24
f(5)=f(4)-8
= f(1)-24-8
=f(1)-32
f(6)=f(5)-8
=f(1)-32-8
=f(1)-40
=100-40
= 60
Hence, Value of f(6) given f(1)=100 is:
60
F(2) = f(1) - 8 = 100-8 = 92
f(3) = f(1) - 2(8) = 100-16 = 84
so f(6) = f(1) - 5(8) = 60
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