Question

Help please look at the image and also use these terms recursive: f(1) = 2, f(n) = 2*f(n-1). explicit: we need to take 1st term/pattern.

Answer 1

The explicit formula for a geometric sequence is given by:

$f(n)=f(1)r^{n-1}$

where r is the common ratio of the sequence.

For this sequence the common ratio is 2 and the first term is 2, therefore its explicit formula is:

$f(n)=2(2)^{n-1}$

The recursive formula for a geometric sequence is given by:

$\begin{gathered} f(1) \\ f(n)=rf(n-1) \end{gathered}$

Therefore in this case we have:

$\begin{gathered} f(1)=2 \\ f(n)=2f(n-1) \end{gathered}$