Solution:
The given sequence is 2, 4, 8, 16, 32, ….
First we have to determine the common ratio and check if they are equal
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r2 = 8/4 = 2
r3 = 16/8 = 2
r4 = 32/16 = 2
As r1 = r2 = r3 = r4 it is a geometric sequence
We know that the formula which can be used is
an = a1 rn - 1
r = 2
Consider number of terms = n
a1 = 2
Substituting the values in the formula
an = 2 (2)n - 1
It can be written as
an = 21.(2)n - 1
an = (2)n - 1 + 1
an = 2n
Therefore, the general term is an = 2n.
Summary:
The general term for the sequence 2, 4, 8, 16, 32, . . . is an = 2n.
