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Answer:
[tex]n_{4} = 8\\ n_{5} = 16[/tex]
Formula: [tex]f(n) = 2^{n-1}[/tex]
Step-by-step explanation:
Derive a rule from the numbers in the sequence:
[tex]n_{1} = 1\\n_{2} = 2\\n_{3} = 4[/tex]
We can see that each number is double of the previous. We can write an explicit function describing this sequence:
[tex]f(n) = 2^{n-1}[/tex] where 'n' is the term number.
Substitute in to solve for the 4th and 5th terms:
[tex]f(4) = 2^{4-1} = 2^{3} =8[/tex]
[tex]f(5) = 2^{5-1} = 2^{4} =16[/tex]
Therefore:
[tex]n_{4} = 8\\ n_{5} = 16[/tex]
