*The numbers of a sequence are called terms where the th term of a sequence is denoted by the symbol .*

A rule can be used which enables any term of a geometric sequence where we know the value of and to be found.

Where is the th term

is the first term

is the common ratio

**Find the 13th term of the geometric sequence ****9, 27, 81, 243, 729, …**

Use the rule:

The value of the 13th term is 4 782 969.

**The 3rd term of a geometric sequence is 32 and the 6th is 2 048. Find the 12th term of this sequence.**

We know that and that .

We know that and that .

We have two different equations so we need to solve them simultaneously.

**[1]**

**[2]**

**[2]** **[1] **

Now that we know the value of , we can substitute it into either equation [1] or [2] to find the value of .

Using the rule, we can now calculate the value of

The 12th term in the sequence is 8 388 608.

Geometric Sequences

Sum of a Finite Geometric Sequence

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