*When the terms of a geometric sequence are added together, a geometric series is formed.*

## Sequence Versus Series

is a *finite* geometric *sequence.*

is a *finite* geometric *series.*

## Turning a Sequence into a Series

The sum of terms, , of a geometric sequence equals:

if or (eg. )

if (eg. )

### Example 1

**Find the sum of the first ten terms of the sequence to five decimal places.**

As , use the second equation.

The question says that we need to answer to five decimal places so:

The sum of the first ten terms is 0.49999.

The sum can be a positive or a negative number.

### Example 2

**The second term of a geometric is 22 and the fifth term is -176. Find the sum of the first eight terms of the sequence correct to one decimal place.**

We need to find the value of and .

So far we have this information:

**[1] **

**[2] **

To find , we need to solve these two equations simultaneously.

Now that we have the value of , we can substitute it into either of the equations to find the value of .

**[1] **

We know know each of the values so we can substitute these into the equation. As , use the first equation.

The question asked for the answer *correct to one decimal place*.

The sum of the first eight terms of the geometric series is -469.3.

#### See also

Geometric Sequences

Finding the Terms of a Geometric Sequence

Sum of an Infinite Geometric Sequence

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