Question

Find the term to term rules for the following sequence-

2,6,18,54,162

Answer 1

`a_n=2*3^(n-1)`

Explanation:

The formula for a geometric sequence is
`a_n=a_1*r^(n-1)` where
`a_n` is the
`n`th term of the sequence,
`a_1` is the first term, and
`r` is the common ratio.

Since each term is being multiplied by 3, this is our common ratio.

Therefore, our geometric sequence formula is
`a_n=2*3^(n-1)`

Answer 2

Essentially, to find the next term in this sequence, the number must be multiplied by 3.

So, the term to term rules for this sequence would be N x 3