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

1 Answer
Jun 24, 2018

14581458

Explanation:

How do we get from 22 to 66? One way is to multiply by 33.

How do we get from 66 to 1818? We can multiply by 33 once again.

What about 1818 to 5454? Again, we can multiply by 33.

We notice that our common ratio is 33. 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!