How do you find the nth term rule for -3,12,-48,192,...?

Aug 26, 2016

${t}_{n} = \frac{3}{4} {\left(- 4\right)}^{n}$.

Explanation:

Let us denote, by ${t}_{n}$, the ${n}^{t h}$ term of the seq.

We find that, ${t}_{2} / {t}_{1} = - 4 , {t}_{3} / {t}_{2} = - 4 , {t}_{4} / {t}_{3} = - 4 , \ldots$

We conclude that the given seq. is a Geometric Seq., with,

${t}_{1} = - 3 , \text{&, common ratio r=-4}$

The Formula for the General Term ${t}_{n}$ for a Geo. Seq. is,

${t}_{n} = {t}_{1} \cdot {r}^{n - 1} = - 3 \cdot {\left(- 4\right)}^{n - 1} = \frac{3}{4} {\left(- 4\right)}^{n}$.

Enjoy Maths.!