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Solution - Geometric Sequences

The common ratio is: r=0.5142857142857142
r=0.5142857142857142
The sum of this series is: s=106
s=106
The general form of this series is: an=700.5142857142857142n1
a_n=70*0.5142857142857142^(n-1)
The nth term of this series is: 70,36,18.514285714285712,9.521632653061221,4.896839650145771,2.5183746772178246,1.295164119712024,0.6660844044233265,0.34255769370342504,0.17617252819033286
70,36,18.514285714285712,9.521632653061221,4.896839650145771,2.5183746772178246,1.295164119712024,0.6660844044233265,0.34255769370342504,0.17617252819033286

Step-by-step explanation

Why learn this

Geometric sequences are commonly used to explain concepts in mathematics, physics, engineering, biology, economics, computer science, finance, and more, making them a very useful tool to have in our toolkits. One of the most common applications of geometric sequences, for example, is calculating earned or unpaid compound interest, an activity most commonly associated with finance that could mean earning or losing a lot of money! Other applications include, but are certainly not limited to, calculating probability, measuring radioactivity over time, and designing buildings.

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