# For a geometric sequence, t8 = 60 and t6 = 72, how do you find t10?

Apr 22, 2016

${T}_{10} = 50$

#### Explanation:

The general formula for the $n t h$ term in a geometric sequence is this: ${T}_{n} = a {r}^{n - 1}$
${T}_{8} = a {r}^{7} = 60$
${T}_{6} = a {r}^{5} = 72$, and know we have to solve for $r$, and we can do this by using the two information we have:
${T}_{8} / {T}_{6} = \frac{60}{72} = \frac{a {r}^{7}}{a {r}^{5}} = {r}^{2}$
$\frac{60}{72} = {r}^{2}$
$\frac{5}{6} = {r}^{2}$
As you'll see, we don't need to square root ${r}^{2}$:
${T}_{10} = a {r}^{9}$
$= a {r}^{7} \cdot {r}^{2}$
$= {T}_{8} \cdot {r}^{2}$
$= 60 \cdot \frac{5}{6}$
$= 50$