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

1 Answer
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:

...54, (54*3), (54*3^2), color(blue)((54*3^3))

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

54*3^3, which is equal to

54*27=color(blue)(1458)

Hope this helps!