What Is the General Formula for the Sequence 2, 6, 10, 14?
Learn how to find the general formula for the sequence 2, 6, 10, 14 using the expression 4n - 2, where n is the term position.
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The general formula for the sequence 2, 6, 10, 14 is 4n - 2, where n represents the position of the term in the sequence. For example, when n is 1, the term is 4(1) - 2 = 2; when n is 2, the term is 4(2) - 2 = 6, and so forth.
FAQs & Answers
- How do you find the general formula for an arithmetic sequence? To find the general formula for an arithmetic sequence, determine the common difference and use the formula an = a1 + (n - 1)d, where a1 is the first term, d is the difference, and n is the term number.
- What does the formula 4n - 2 represent in a sequence? The formula 4n - 2 represents an arithmetic sequence where each term increases by 4 starting from the first term 2, corresponding to term positions n = 1, 2, 3, and so on.
- Can all sequences be expressed using a general formula? Not all sequences have a simple general formula, but many arithmetic and geometric sequences do. Some complex sequences may require recursive definitions or advanced formulas.