# Here is the formula you need: *Know it. Love it. - PowerPoint PPT Presentation

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Sometimes we are interested in not only finding a specific term in the sequence but then sum of the first few terms of the sequence. For example : If you are paying off your credit card, you might be interested in how much you pay overall for the item not just how much you pay each month.

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Here is the formula you need: *Know it. Love it.

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#### Presentation Transcript

Sometimes we are interested in not only finding a specific term in the sequence but then sum of the first few terms of the sequence.

For example: If you are paying off your credit card, you might be interested in how much you pay overall for the item not just how much you pay each month.

Here is the formula you need:

*Know it. Love it.

r: common ratio

n: number of terms

a: starting value

S: sum

Let’s try one:

You have a job that pays you a salary of \$20,000 and gives a raise of 3% every year based on performance. How much money will you acquire over the next 5 years?

## Sum of a Finite Geometric Sequence

We are going to guide you through the proof of finding the sum. We will ask you to be an active participant.

Let

Now multiply each side by r. (Distribute the r)

What did you get?

Now subtract ( be sure you subtract the entire rS)

You should have:

Now simplfy (combine like terms) :

Factor out an S

Divide: