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Find the explicit formula for the sequence? -1,4,16,64

User Serlingpa
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1 Answer

4 votes

Answer:


f(n)=4^(n-1)

Step-by-step explanation:

Given the sequence


1,4,16,64

We observe that the next term of the sequence is obtained by multiplying the previous term by 4.

This is an example of a geometric sequence.

The nth term of a geometric sequence is:


\begin{gathered} U_n=ar^(n-1) \\ \text{First term, a=1} \\ \text{Common ratio, r =4} \end{gathered}

Therefore, the nth term is:


U_n=1*4^(n-1)

The explicit formula for the sequence is:


f(n)=4^(n-1)

User PhillyNJ
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