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3 years ago

If f(1)=6f(1)=6 and f(n)=nf(n-1)-4f(n)=nf(n−1)−4 then find the value of f(3)f(3).

Mathematics

2 answers:

nekit [7.7K]3 years ago

8 0

Answer:6144

Step-by-step explanation:

If f(1)=6f(1)=6 and f(n)=4f(n-1)f(n)=4f(n−1) then find the value of f(6)f(6).

f(1)=

\,\,6

f(\color{darkgreen}{2})=

f(2)=

\,\,4f(\color{darkgreen}{2}-1)

4f(2−1)

\,\,4f(1)

4f(1)

\,\,4(6)

4(6)

Substitute f(1)=6

f(2)=

\,\,24

f(\color{darkgreen}{3})=

f(3)=

\,\,4f(\color{darkgreen}{3}-1)

4f(3−1)

\,\,4f(2)

4f(2)

\,\,4(24)

4(24)

Substitute f(2)=24

f(3)=

\,\,96

f(\color{darkgreen}{4})=

f(4)=

\,\,4f(\color{darkgreen}{4}-1)

4f(4−1)

\,\,4f(3)

4f(3)

\,\,4(96)

4(96)

Substitute f(3)=96

f(4)=

\,\,384

384

f(\color{darkgreen}{5})=

f(5)=

\,\,4f(\color{darkgreen}{5}-1)

4f(5−1)

\,\,4f(4)

4f(4)

\,\,4(384)

4(384)

Substitute f(4)=384

f(5)=

\,\,1536

1536

f(\color{darkgreen}{6})=

f(6)=

\,\,4f(\color{darkgreen}{6}-1)

4f(6−1)

\,\,4f(5)

4f(5)

\,\,4(1536)

4(1536)

Substitute f(5)=1536

f(6)=

\,\,6144

6144

\text{Geometric Sequence:}

Geometric Sequence:

Common ratio of 4

6,24,96,384,1536,6144, ...

6,24,96,384,1536,6144,...

\text{Final Answer:}

Final Answer:

6144

alekssr [168]3 years ago

6 0

Answer:

Step-by-step explanation:

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