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Geometric Sequences and Series. 1. Write the first four terms of the following G.S. a 5, r 1/4, ,, 2. What is the value of the sixth term if a 5 and r 2/3? 3. Which term of the geometric sequence
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How to fill out geometric sequences and series

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How to fill out geometric sequences and series?

01
Identify the first term, a, of the sequence. This is the starting value.
02
Determine the common ratio, r, of the sequence. This is the constant factor between each term.
03
Write out the sequence by multiplying the first term by the common ratio repeatedly. For example, if the first term is 2 and the common ratio is 3, the sequence would be 2, 6, 18, 54, ...
04
To fill out a geometric series, add up all the terms in the sequence. This can be done using the formula S = a * (1 - r^n) / (1 - r), where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

Who needs geometric sequences and series?

01
Students studying mathematics or algebra may need to understand and work with geometric sequences and series as part of their curriculum.
02
Scientists and researchers often encounter geometric sequences and series in various fields such as physics, biology, and finance. These sequences can help model and analyze phenomena like population growth, radioactive decay, and compound interest.
03
Engineers and technicians may use geometric sequences and series to solve problems related to exponential growth or decay, such as calculating the value of electrical currents or the degradation of materials over time.
In summary, understanding how to fill out geometric sequences and series is important for students, scientists, researchers, engineers, and technicians in various fields where exponential growth or decay is observed or analyzed.

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