Explanation:
Step 1. The recursive formula that we have is:
[tex]\begin{gathered} h(1)=1, \\ h(n)=2\cdot h(n-1) \\ for\text{ n}\ge2 \end{gathered}[/tex]
where h(n) is the value of h (the sequence) for a certain n value, and h(1) represents the first value of the sequence. In this case h(1)=1 tells us that the first value must be 1, and this discards the first sequence option.
DISCARDED: 80, 40, 20, 10, 5
because the first value must be 1.
Step 2. Now, using the formula
[tex]h(n)=2\cdot h(n-1)[/tex]
We can find the second value of the sequence by using n=2
[tex]h(2)=2\cdot h(2-1)[/tex]
Step 3. Simplifying:
Step 4. finally, since we know that h(1)=1
The second term must be 2, this is only true for the second option:
1,2,4,8,16.
Answer:
1, 2, 4, 8, 16.
