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Excel in math and science
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Geometric Progressions
A geometric progression is a sequence of numbers where the previous term is multiplied by a constant to get the next term. 1, 2, 4, 8,... is a geometric sequence where each term is multiplied by 2.
Excel in math and science
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Concept Quizzes
Evaluate
\[ 1 + 2 + 2^2 + 2^3 + \ldots + 2^{ 24 }. \]
Excel in math and science
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A bookshelf has \(6\) shelves. The top shelf has \(2\) books, and each other shelf has \(3\) times as many books as the shelf directly above it. If you want to read a book from the shelves, how many choices do you have?
Details and assumptions
All of the books are different.
Excel in math and science
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The series \(a_1, a_2, a_3, a_4, a_5, a_6, a_7\) is a geometric progression with \(a_4 = 48\) and \(a_5 = 96\). What is the sum of the these \(7\) terms?
Details and assumptions
A geometric progression is a sequence of numbers, in which each subsequent number is obtained by multiplying the previous number by a common ratio / multiple. For example, \(1, 2, 4, 8, 16, 32, 64, \ldots \) is a geometric progression with initial term 1 and common ratio 2.
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Consider a geometric progression with initial term \(4\) and common ratio \(5\). What is the smallest value of \(n\) for which the sum of the first \(n\) terms is greater than \(800\)?
Excel in math and science
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Evaluate the sum to infinity:
\[ \frac{ 14 } { 2^0} + \frac{ 14 } { 2^1 } + \frac{ 14 } { 2^2 } + \ldots .\]