Question

Find an explicit formula for the geometric sequence 2, 6, 18, 54, ....
Note: the first term should be b(1).

b(n)=

Answer 1

The geometric sequence can be represented explicitly or as recursions

The explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)

How to determine the explicit formula?

The sequence is given as:

2, 6, 18, 54, ....

Start by calculating the common ratio (r)

r = b2/b1

This gives

r = 6/2

Evaluate the quotient

r = 3

A geometric sequence is represented as:

b(n) = b1 * r^(n-1)

This gives

b(n) = 2 * 3^(n-1)

Hence, the explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)

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