Question

What is the 13th term of the geometric sequence 4, 12, 36, 108, ...?

Answer 1

Answer: 2,125,764

Step-by-step explanation:

You can use the equation y=ar^n-1 to find the 13th term where a is the starting term, r is the common ratio, and n is the nth term

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. Therefore the equation is:

y=4*3^(n-1)

Substitute 13 for n:

y=4*3^(13-1)

y=4*3^12

y=2125764

Therefore, the 13th term of this geometric sequence is 2,125,764