Question

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 2, 4, 8, 16, 32, 64

Answer 1

It is a geometric sequience.
the general term (an) is:
an=a₁*r^(n-1)
a₁ is the first term=2
r=the common ratio=a₂ / a₁=4/2=2
therefore:

an=2*2^(n-1)
an=2^(n-1)+1
an=2^n

solution: an=2^n

To check
a₁=2¹=2
a₂=2²=2*2=4
a₃=2³=2*2*2=8
a₄=2⁴=2*2*2*2=16  ....