Question

Find the generating function for the finite sequence 1, 4, 16, 64, 256.

Answer 1

Answer:

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Step-by-step explanation:

f = (4n)²

Answer 2

$f(n)=4^{n-1}$ where$1\leq n\leq 5$

Step-by-step explanation:

Given sequence

1,4,16,64,256

$a_1=1=4^0$

$a_2=4=4^1$

$a_3=16=4^2$

$a_4=64=4^3$

$a_5=256=4^4$

From above pattern we can write as

$a_n=4^{n-1}$

Where $1\leq n\leq 5$

Therefore, the function for the given finite sequence is given by

$f(n)=4^{n-1}$ where$1\leq n\leq 5$

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