If a geometric sequence has a common ratio of 4 and if each term of the common ratio of the resulting sequence?

Answer 1

I don't quite understand your question. Please make sure you typed it correctly.

If the sequence is a geometric sequence, then to go from one term to the next, I multiply by the common ratio. In this case, since the common ration is 4, I multiply each term by 4 to get to the next term.

One way of expressing that is to use what's called a recursive equation. A recursive equation requires you to know what term you are on and then it allows you to find the next term (in this case by multiplying by 4).

If we define the "term we are on" as t_n then the next term would be one more from that or t_n+1. So we could write:

The next term (t_n+1) is the term we are on (t_n) * 4 or:

t_n+1 = t_n * 4 or

t_n+1 = 4t_n

But I'm not sure if that answers your question or not. : (