The given formula of geometric sequence is:
[tex] a_{n}=2(2)^{n-1} [/tex]
The general formula of a geometric sequence is:
[tex] a_{n}= a_{1}(r)^{n-1} [/tex]
Comparing the given equation with general equation, we can write:
a₁ = First Term = 2
r = Common Ratio = 2
In a geometric sequence each term is obtained by multiplying the previous term by the Common Ratio. So for the given sequence, each next term will be obtained by multiplying the previous term by 2.
So, nth term will be obtained my multiplying the (n-1)th term by 2.
Therefore, the recursive formula of the given geometric sequence will be:
[tex]a_{n}=2* a_{n-1} [/tex]
Therefore, option B gives the correct answer
