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Real-life Geometric and Arithmetic Sequences
87
Equations Continued
Summation Notation:
Visual Representation
In this graph each bar is increasing by 15% each time. This creates the sequence of 1,1.2,1.3,1.4.....
Geometric Sequence
You want to run a 10 mile race. But you have never ran long distance before. To accomplish this goal you need to build up the endurance and stamina to attain this goal. You start at 1 mile of running your first week. The next week week you decide to increase your miles by 15% every week. Then the next week you would be running 15% more than last week. You continue to increase your miles until you have reached your goal of 100% or your 10 mile goal.
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Summation Notation
Visual Graph
Equations
Explicit formula: an = a1 + (n – 1)d
n= the term we are trying to find
a1= The first term (1)
d= the common difference (1)
With this information we can plug in our known information to create the formula
an = 1 + (n-1) 1
In this graph its representing each bar increasing by one mile each time. This creates the arithmetic sequence of 1,2,3,4,5.....
Arithmetic Sequence Situation
Real-life Geometric and Arithmetic Sequences
References
Some ideas for the real-life example were expanded from the ideas of Jasmine Johnson prezi "Real- life Geometric and Arithmetic Sequences" prezi.com/zz7oomagwd-_/real-life-geometric-and-arithmetic-sequences
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Recursive formula: a1 = ?
an= an-1 + d
With the information provided, we can plug it in the known information to create the equation
a1 = 1
an = an-1 + 1
Equations Continued
Equations
Recursive formula:
a1 = ?
an = (an-1) r
With the data provided, we can plug in our known data to create the equation
a1 = 1
an = (an-1) 1.15
explicit formula: an = a1 * rn-1
n= the term we are trying to find
a1= the first term
r = common ratio
With this data, we can replace our known data to create the equation
an = 1 * 1.15n-1