STEP 1: Recall what is a sequence

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STEP 2: Recall what is a geometric sequence

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STEP 3: The recursive formula for a geometric sequence is written in the form

a_{n} = a_{n-1}.r

For our particular sequence, if the common ratio (r) is 3, we would write

a_{n} = a_{n-1}.3

So once you know the common ratio in a geometric sequence you can write the recursive form for that sequence.

Rather than write a recursive formula, we can write an explicit formula. The **explicit formula** is also sometimes called the closed form. To write the explicit or closed form of a geometric sequence, we use

a_{n} = a_{1}.r^{n-1}

a_{n} is the nth term of the sequence

a_{1} is the first term in the sequence

r is the common ratio for the geometric sequence

n is treated like the variable in the sequence

Skills to recall:

What is a variable in the sequence