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# Mariana project reality-series

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### Mariana project reality-series

1. 1. Project:Reality series by:Mariana Rosales
2. 2. What is a geometric and aritmetic  sequence? <ul><ul><li>A geometric sequence   is a group of numbers that are that can be found by multipying the previous number by a common ratio. </li></ul></ul><ul><ul><li>Arithmetic sequence is a group of numbers that have a  difference between the consecutive terms  which is a  constant. </li></ul></ul><ul><li>  </li></ul>
3. 3. The real life example of arithmetic sequence. <ul><li>  </li></ul><ul><li>The chess is a real life example of arithmetic sequence because when the horse moves it goes by threes so it increases with a common ratio . The same thing happens when it goes backwards but the only difference is that you divide . </li></ul><ul><li>  </li></ul><ul><li>  </li></ul>
4. 4. Other examples of arithmetic sequence. <ul><li>When a car speeding 10 km per minute tha means the car will form an arithmetic sequence because every minute will add 10 km . Same thin happens when decelerating because it makes the rest of 10 km per minute. </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><ul><li>Un=U1+(n-1)d </li></ul></ul><ul><li>  </li></ul><ul><li>         Un=0+(11-1)10 </li></ul><ul><li>         Un=100 </li></ul><ul><li>   </li></ul><ul><li>2. Sn=11/2(2(o)+(11-1)10)=11/2(0+100) </li></ul><ul><li>      Sn=550 </li></ul>
5. 5. The real life example of geometric sequence. <ul><li>Suppose that you invest \$2000 in the bank for 2 years , but this time you are paid a compound interest rate of 20 %pa. The interest is added to your investment each year, and now you are paid interest. </li></ul><ul><li>  </li></ul><ul><li>This suggest that if the money is left in your account for n years it would amount to \$2000 x (2.1)n. </li></ul><ul><li>U1=\$2000            initial investment </li></ul><ul><li>U2=U1x 2.1          amount after 1 year </li></ul><ul><li>U3=U1x(2.1)2      amount after 2 years </li></ul><ul><li>U4=U1x(2.1)3      amount after 3 years </li></ul><ul><li>                                     </li></ul><ul><li>                             Un+1=U1x(2.1)n= amount after n years. </li></ul>
6. 6. Process of the project <ul><ul><li>Wha mathematical concepts were illustrates in the Reality Seris Project? </li></ul></ul><ul><li>  </li></ul><ul><li>The mathematical concepts that were illustrates in the reality series project were geometric sequences and arithmetic sequences.Geometric sequences is the each term after the first is found by multiplying the previous one by the common ratio and the arithmetic sequences is a sequence of numbers that has a different between the consecutive terms which make it a  constant. </li></ul><ul><li>  </li></ul>
7. 7. <ul><ul><li>What problems did you encounter as you complete the project? </li></ul></ul><ul><li>  </li></ul><ul><li>I got troubles trying to find a real life example of geometric sequences because we usually have more arithmetics examples in real life. </li></ul><ul><li>  </li></ul><ul><ul><li>How did you solve these problems? </li></ul></ul><ul><li>  </li></ul><ul><li>What I did to find a solution was to analyzed what I usually do in my spare time and I used to play chess in my other school. </li></ul><ul><li>  </li></ul><ul><ul><li>How did your group work together to complete the project? </li></ul></ul><ul><li>  </li></ul><ul><li>I did it along becuase it was a individually project. </li></ul><ul><li>  </li></ul><ul><ul><li>What did you learn from this project? </li></ul></ul><ul><li>  </li></ul><ul><li>I learned from this project that we use arithmetic and geometric sequences in our daily lives. </li></ul>
8. 8. References <ul><ul><li>Information: </li></ul></ul><ul><li>  </li></ul><ul><li>http://www.themathpage.com/arith/arithmetic.htm </li></ul><ul><li>  http://www.mathwords.com/a/arithmetic_sequence.htm </li></ul><ul><li>  http://www.algebralab.org/lessons/lesson.aspx?file=algebra_geoseq.xml </li></ul><ul><li>  </li></ul><ul><ul><li>Images were taken from google images. </li></ul></ul><ul><li>  </li></ul>