Geometric Sequence

Mining engineering is an engineering discipline that involves the practice, the theory, the science, the technology, and application of extracting and processing minerals from a

naturally occurring environment.

The mine worker was working alone and suddenly he found an ore sample of radioactive material.

He discovered that an ore sample of radioactive material is containing 500 mg.

A mine worker discovers an ore sample containing

500 mg of radioactive material.  It is discovered

that the radioactive material has a half life of 1 day.  Find the amount of

radioactive material in the sample at the

beginning of the 7th day.

LEARNING GEOMETRIC SEQUENCE

YES

Hi I’m Alden. Would you help me to find the amount of radioactive material in the sample at the beginning of the 7th day?

Hi, Im Maine. Would you like to help us to solve our problem?

Great! Thank you very much for helping us in solving our problems.

Hi! Welcome. I think the GEOMETRIC SEQUENCE will help us to solve the problems easier. But did you know the Geometric Sequence already?

I don’t know what it is. But let’s find out the meaning of it and how it is related in solving our problems! Would you like to come with me?

WHAT IS GEOMETRIC SEQUENCE?

If a sequence of values follows a pattern ofmultiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a geometric sequence.   The number multiplied each time is constant (always the same).The fixed amount multiplied is called the common ratio, r, referring to the fact that the ratio (fraction) of the second term to the first term yields this common multiple.  To find the common ratio, divide the second term by the first term.

Notice the non-linear nature of the scatter plot of the terms of a geometric sequence.  The domain consists of the counting numbers 1, 2, 3, 4, ... and the range consists of the terms of the sequence.  While the x value increases by a constant value of one, the y value increases by multiples of twoEXAMPLE:5, 10, 20, 40, ...

r = 2

FORMULA:

multiply each term by 2 to arrive at the next termor...divide a2 by a1 to find the common ratio, 2.

LET’S GO BACK?

SURE MAINE!

PROBLEM:A mine worker discovers an ore sample containing 500 mg of

radioactive material.  It is discovered that the radioactive material has a

half life of 1 day.  Find the amount of radioactive material in the sample at

the beginning of the 7th day.

500 mg of ore.  Half life of one day means that half of the amount remains after 1 day.

Begin of day 1500 mg

Begin of day 2250 mg

Begin of day 3125 mg …..

End of day 1250 mg

End of day 2125 mg

End of day 362.5 mg

…..

Decide to either work with the "beginning" of each day, or the "end" of each day, as each can yield the answer.  Only the starting value and number of terms will differ.  We will use "beginning":

LET’S TRY!

?

A. 7.8120mg

CHOICES:

B. 7.8126mgC. 7.8125mgD. 7.8124mg

C. 7.8125

So the answer is 7.8125mg

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ANA MAE BRISTOL

NAME:

Section: X- RUBYTeacher: Mr. Eric De Guzman

GEOMETRIC SEQUENCE