Question

If the sequence 2, 2, 4, 6, 10,... were to follow the same pattern as the Fibonacci sequence, what are the next three terms?A. 14,20,26B.14,22,30C.16,26,36D.16,26,42

Answer 1

Okay, here we have this:

Considerando que la sucesión fibonacci sigue el siguiente patrón:

`f_n=f_(n-1)+f_(n-2)`

So, we need to find the terms 6th, 7th, 8th; let's do it:

Term 6th:

`\begin{gathered} f_6=f_5+f_4 \\ f_6=10+6=16 \end{gathered}`

Term 7th:

`\begin{gathered} f_7=f_6+f_5 \\ f_7=16+10=26 \end{gathered}`

Term 8th:

`f_8=f_7+f_6=26+16=42`

Finally we obtain that the correct answer is the option D.