Question

The 13th term of this geometric sequence is 16,384 and the first term is 4. what is the common ratio

Answer 1

A geometric sequence is a sequence with a common ratio multiplied by previous term to give the next. Lets call x the common ratio, so we know that 4 was multiplied by x to give the second term, and so forth until it was multiplied again and again by x until the 16384 was reached which happens to be the 13th term, that means that 4x was multiplied by x 12 more times to give 16384, that is:
4x^12 = 16384
x^12 = 4096
x = 4096^-12
x = 4.48 x 10^-44
that is the common ratio