# How do I find the 6th term of the geometric sequence for which t_3 = 444 and t_7 = 7104?

May 11, 2015

${t}_{6} = 3552$

First you have to calculate $r$. To do so you can use the formula

${t}_{7} = {t}_{3} \cdot {r}^{4}$, so $r = \sqrt[4]{\frac{{t}_{7}}{{t}_{4}}} = 2$. Now you can calculate ${t}_{6} = {t}_{7} / r = \frac{7104}{2} = 3552$