Find an explicit formula for the geometric sequence with a_{2}=12 and a_{4}=48

Guest May 7, 2021

#1**0 **

First thing I see is that we can take 12 out of both of them, that's helpful.

a2 is 1, a4 is 4.

2^0 is 1, and 2^2 is 4, that's a helpful fact... but our subscripts were 2 and 4, not 0 and 2. We could shift them by using 2^(x - 2). Thus:

\(12 * 2^{x-2}\)

I suppose 2^x * 2^-2 is basically 2^x / 4, so we could simplify further to:

\(3 * 2^{x}\)

Guest May 7, 2021