Answer: 1536
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Work Shown:
Replace n with 2
f(n) = 4*f(n-1)
f(2) = 4*f(2-1)
f(2) = 4*f(1)
f(2) = 4*6 ................. replace f(1) with 6; since f(1) = 6
f(2) = 24
Repeat for n = 3
f(n) = 4*f(n-1)
f(3) = 4*f(3-1)
f(3) = 4*f(2)
f(3) = 4*24 ................. replace f(2) with 24; since f(2) = 24
f(3) = 96
Plug in n = 4
f(n) = 4*f(n-1)
f(4) = 4*f(4-1)
f(4) = 4*f(3)
f(4) = 4*96 ................. replace f(3) with 96; since f(3) = 96
f(4) = 384
And finally n = 5
f(n) = 4*f(n-1)
f(5) = 4*f(5-1)
f(5) = 4*f(4)
f(5) = 4*384 ................. replace f(4) with 384; since f(4) = 384
f(5) = 1536 which is the final answer
The sequence is: 6, 24, 96, 384, 1536, ....
As you can see, each new term of the recursive sequence is built off the previous one.
Each time we need a new term, we multiply by 4.
The closed form equation is
If you plugged in n = 5, then
For more information, search out geometric sequences.