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How do you find a term in a arithmetic sequence?
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An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same. Generally, the arithmetic sequence is written as a, a+d, a+2d, a+3d, ..., where a is the first term and d is the common difference.
Arithmetic Sequences. If the term-to-term rule for a sequence is to add or subtract the same number each time, it is called an arithmetic sequence, eg: 4, 9, 14, 19, 24, ... or 8,...
Learn the definition and basic examples of an arithmetic sequence, along the concept of common difference. Understand how the terms in an arithmetic sequence are generated, and the difference between increasing and decreasing sequences.
- continuing an arithmetic sequence. Calculate the next three terms for the sequence 4, 7, 10, 13, 16, … Take two consecutive terms from the sequence.
- continuing an arithmetic sequence with negative numbers. Calculate the next three terms for the sequence -3, -9, -15, -21, -27, … Take two consecutive terms from the sequence.
- continuing an arithmetic sequence with decimals. Calculate the next three terms for the sequence 0.1, 0.3, 0.5, 0.7, 0.9, … Take two consecutive terms from the sequence.
- continuing an arithmetic sequence involving fractions. Calculate the next three terms for the sequence. \[\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2}, \ldots\]
An arithmetic sequence is a type of sequence in which the difference between each consecutive term in the sequence is constant. For example, the difference between each term in the following sequence is 3: 2, 5, 8, 11, 14, 17, 20...
Arithmetic sequences (arithmetic progressions) are ordered sets of numbers that have a common difference (d) between each consecutive term. If you add or subtract the same number each time to make the sequence, it is an arithmetic sequence. For example, A recursive formula uses the previous number in the sequence to determine the successive number.
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
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