# What is the 7th term of this geometric sequence 2, 6, 18, 54, …?

Jun 24, 2018

$1458$

#### Explanation:

How do we get from $2$ to $6$? One way is to multiply by $3$.

How do we get from $6$ to $18$? We can multiply by $3$ once again.

What about $18$ to $54$? Again, we can multiply by $3$.

We notice that our common ratio is $3$. We can leverage this fact to write the next terms of our sequence:

$\ldots 54 , \left(54 \cdot 3\right) , \left(54 \cdot {3}^{2}\right) , \textcolor{b l u e}{\left(54 \cdot {3}^{3}\right)}$

Notice, we are multiplying by three every time. The $7$th term of this sequence is given by the blue expression

$54 \cdot {3}^{3}$, which is equal to

$54 \cdot 27 = \textcolor{b l u e}{1458}$

Hope this helps!