# If a_n=1/3*6^(n-1), what is a_6?

Oct 20, 2016

${a}_{6} = 2592$

#### Explanation:

If ${a}_{n} = \frac{1}{3} \cdot {6}^{n - 1}$,

we can find ${a}_{6}$ by substituting $n$ by $6$.

Hence ${a}_{6} = \frac{1}{3} \cdot {6}^{6 - 1}$

= $\frac{1}{3} \cdot {6}^{5}$

= $\frac{6 \times 6 \times 6 \times 6 \times 6}{3}$

= $\frac{2 \cancel{6} \times 6 \times 6 \times 6 \times 6}{1 \cancel{3}}$

= $2592$