# How do you find the indicated term of the geometric sequence where a_1=16,807, r=3/7, n=6?

Nov 27, 2017

${T}_{n} = {T}_{6} = 243$

#### Explanation:

General form of geometric sequence is $a , a r , a {r}^{2} , a {r}^{3} , . . . a {r}^{n - 1}$
${T}_{n} = a {r}^{n - 1}$ where 'a' stands for first term ${a}_{1}$
Given a_1 = 16807, r = (3/7) & n = 6
$\therefore {T}_{6} = 16807 \cdot {\left(\frac{3}{7}\right)}^{6 - 1}$
${T}_{6} = \frac{16807 \cdot {3}^{5}}{7} ^ 5$
${T}_{6} = \frac{\cancel{16807} \cdot 243}{\cancel{{7}^{5}}}$ as 7^5 = 16807 & 3^5 = 243
${T}_{6} = 243$