# Week 2 – Geometric Sequence

This week, I have learned how to solve a geometric sequence. The difference between geometric and arithmetic is that you have addition for arithmetic and multiplication on geometric.

Vocabulary

Geometric sequence : In geometric sequence, you use the formula,

$t_n=t_1r^{n-1}$

$t_1$ is the first term and r is the common ratio.

To find the common ratio, you divide the second term from the first term.

Example:

r=$\frac{t_2}{t_1}$

r=$\frac{6}{3}$

r= 2

So, if you have $t_1$ as 5 and your common ratio is 2, you would have something like this.      5, 10, 20, 40, 80, 160

Now lets have a practice. 2, 4, 8, 16, 32, 64 …

Let’s find the $t_8$

r=2    $t_1$ = 2   n= 8

$t_n=t_1r^{n-1}$

$t_8=2(2^{8-1})$

$t_8=2(128)$

$t_8=256$

Its simple as that. Next week, we will look at something new because we will have a new chapter. Stay tuned