Sequences and Series

The concepts of sequences and series are foundational in the field of mathematics. Essentially, a sequence refers to a structured arrangement of numbers where each one possesses a distinct position. On the other hand, a series is defined as the total sum of the terms within a sequence. These concepts are not limited to a single area of mathematics but are utilized in diverse fields such as algebra, calculus, and number theory.

Arithmetic Sequences/Progressions

In an arithmetic sequence, the first term is 5 and the common difference is 3. What is the 8th term in the sequence?
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Geometric Sequences/Progressions

Find the sum of the first 10 terms of the geometric sequence with first term 3 and common ratio 2.
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Finding the Next Term of the Sequence

Consider the sequence: 3, 6, 12, 24, 48, ___. What is the next term of the sequence?
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Finding the nth Term Given a List of Numbers

Given the sequence 5, 8, 14, 23, 35, ..., find the nth term of this sequence.
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Finding the nth Term

Find the nth term of the geometric sequence 3, 6, 12, 24, ...
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Finding the Sum of First n Terms

Find the sum of the first 10 terms of the arithmetic sequence where the first term is 5 and the common difference is 3.
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Expanding Series Notation

Find the sum of the series: \(\sum_{n=1}^{5} 2n^2 + 3n + 1\)
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Finding the Sum of the Series

Find the sum of the series \(1 + 2 + 4 + 8 + 16 + ... + 1024\)
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Finding the Sum of the Infinite Geometric Series

Find the sum of the infinite geometric series: \(3, 6, 12, 24, ...\)
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