Identify and extend the pattern to find the next number in this sequence: 2, 8, 32, 128, ... A. 152 B. 134 C. 224 D. 512

Given that the sequence is:

2, 8, 32, 128, ...

The series is a geometric sequence because there is a common ratio between the consecutive numbers. Thus it will follow the explicit form given by:

an=ar^ (n-1)

where:

a=first term

r = common ratio

n = nth term

from the sequence:

a=2

r=8/2=4

thus the explicit formula for the sequence is:

an=2 (4^ (n-1))

thus the next term which is the fifth term will be:

a5=2 (4^ (5-1))

a5=512

Answer: D