Sequences as Functions and Recursion
Algebra · Flashcards · Application
ALGEBRA · FLASHCARDS
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QUESTION
What is the value of
f
(
4
)
f(4)
f
(
4
)
for Fibonacci given
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
,
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
,
f
(
n
+
1
)
=
f
(
n
)
+
f
(
n
−
1
)
f(n+1)=f(n)+f(n-1)
f
(
n
+
1
)
=
f
(
n
)
+
f
(
n
−
1
)
?
QUESTION
What is the value of
f
(
3
)
f(3)
f
(
3
)
if
f
(
0
)
=
2
f(0)=2
f
(
0
)
=
2
,
f
(
1
)
=
5
f(1)=5
f
(
1
)
=
5
, and
f
(
n
+
1
)
=
f
(
n
)
+
f
(
n
−
1
)
f(n+1)=f(n)+f(n-1)
f
(
n
+
1
)
=
f
(
n
)
+
f
(
n
−
1
)
for
n
≥
1
n\ge 1
n
≥
1
?
QUESTION
What is the output of the sequence defined by
f
(
n
)
=
n
−
1
2
f(n)=\frac{n-1}{2}
f
(
n
)
=
2
n
−
1
at
n
=
7
n=7
n
=
7
?
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ANSWER
f
(
7
)
=
3
f(7)=3
f
(
7
)
=
3
. Substitute
n
=
7
n=7
n
=
7
:
f
(
7
)
=
7
−
1
2
=
6
2
=
3
f(7)=\frac{7-1}{2}=\frac{6}{2}=3
f
(
7
)
=
2
7
−
1
=
2
6
=
3
.
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