Week 2 – Geometric Sequence

This week we learned how to determine $t_n$ in a geometric sequence.

Using the equation $t_n$ = $t_1$ $r^n-1$ , we can find any term in the geometric sequence.

For example: The geometric sequence is 2, 8, 32…

We can find r, which is the variable for the ratio, by taking the second term and dividing it by the first.

Therefore $\frac{8}{2}$ is the ratio, or 4

Now we know that $t_1$ or the first term is 2

So now we can fill in the equation. Let’s find the 7th term.

$t_7$ = 2 $4^7-1$

$t_7$ = 2 $4^6$

$t_7$ = 2(4096)

$t_7$ = 8192

This equation is very helpful to finding the $t_n$ but it can also be helpful if you need to find another variable and you already know two.

Imagine we already knew $t_7$ and we want to find the first term. Using the equation, we can solve for $t_1$

8192 = $t_1$ $4^7-1$

8192 = $t_1$ $4^6$

8192 = $t_1$ 4096

Now you divide both sides by 4096

2 = $t_1$

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