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

1 Answer
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 nth 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*3^n=1*3^n.
But then the nth term would be t_(n-1) and all would still be correct. Watch this when you're doing a test!