A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula?

–12, –18, –27, ...
–20, 30, –45, ...
–18, –16.5, –15, ...
–16, –17.5, –19, ...

Question

A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula?

–12, –18, –27, ...
–20, 30, –45, ...
–18, –16.5, –15, ...
–16, –17.5, –19, ...

anonymous · Answer

Take the first number in each sequence ($f(1)$) and multiply it by $\dfrac{3}{2}$. Does the next term ($f(2)$) match?

For example, in the second sequence:
$$f(1)=-20\
f(2)=\frac{3}{2}(-20)=-30\neq30$$
That eliminates the second option.