# How do you find the next two terms of the geometric sequence 81, 108, 144,...?

Jan 1, 2017

192; 256

#### Explanation:

${a}_{i + 1} = {a}_{i} \times r$

$\implies r = \frac{{a}_{i + 1}}{a} _ i = \frac{108}{81} = \frac{144}{108} = \frac{4}{3}$

${a}_{1} = 81$
${a}_{2} = 81 \times \frac{4}{3} = 108$
${a}_{3} = 108 \times \frac{4}{3} = 144$
${a}_{4} = 144 \times \frac{4}{3} = 192$
${a}_{5} = 192 \times \frac{4}{3} = 256$

${a}_{n} = 81 \times {\left(\frac{4}{3}\right)}^{n - 1}$