Answer:
Explanation:
First let us look at this sequence. 6, 24, 96, 384, 1536,... There are two sequences that can help us solve this problem. These two sequences are called arithmetic and geometric.
Arithmetic sequence is when the difference is constant, usually the difference, or d, is decreasing or increasing each term.
The formula is a(subscript n)= a(subscript 1) + (n-1)d
With geometric sequence it is when the difference is multiplied or divided each term, and it is represented with a common ratio, or r.
The formula is a(subscript n)= ar^n-1
In this situation, we will be using the geometric sequence because it mentions the common ratio. So let get started..
Step 1: what is the common ratio?
Well let us see how do we get 24 from 6? 24 divided by 6 equals 4! Does it follow for 96 from 24? Well, 96 divided by 4 does equal 24!
There is proof right there that the rule of this sequence is that it multiplies each term by 4. Now we can say that the common ratio is 4.
Sorry for typing quite a bit, I do like to go into details when explaining how I process or work out a problem. If you have any questions or concerns let me know. I hope you have a nice day.