# How do you find a formula of the nth term for this sequence: 1, 3, 9, 27, 81, …?

Feb 12, 2016

Apparently the common ratio is $3$

#### Explanation:

The 2nd term is $3$, the 3rd=$9 = {3}^{2}$, the 4th=$27 = {3}^{3}$
To get to the $n$th term we will have to multiply $n - 1$ times by $3$

Or:
${t}_{n} = {3}^{n - 1}$

Watch out!
Usually the first term is called ${t}_{0}$, which would change the formula into ${t}_{n} = {t}_{0} \cdot {3}^{n} = 1 \cdot {3}^{n}$.
But then the $n$th term would be ${t}_{n - 1}$ and all would still be correct. Watch this when you're doing a test!