# How do you find the 4th, 5th, 6th, and 7th term of the geometric sequence 7, 21, 63...?

Feb 18, 2016

The general term of a geometric sequence of common ratio $r$ and first term $a$ is given by
${T}_{n} = a {r}^{n - 1}$

In this case the first term is $a = 7$ and since it is a geometric sequence, it has a common ratio
$r = \frac{21}{7} = \frac{63}{21} = 3$.

Hence general term ${T}_{n} = 7 \cdot {\left(3\right)}^{n - 1}$.

$\therefore {T}_{4} = 7 \cdot {3}^{4 - 1} = 189$

${T}_{5} = 7 \cdot {3}^{5 - 1} = 567$

Similarly ${T}_{6} = 1701 \mathmr{and} {T}_{7} = 5103$