Question

Find sn for the g.p 4,12,36,108

Answer 1

Consider the given sequence. It starts from the number 4. The next number is 12/4=3 times greater than the first. So if this sequence is a geometric one, then the next term must be 12*3=36. This is true, and the next term must be 36*3=108, which is also true.

Therefore this sequence is a geometric one and its common ratio is 3. We can predict its next terms: 108*3=324, 324*3=972 and so on. The n-th term is

a_n=4*3^(n-1).