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Arithmetic Sequence Formula:
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An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference (d). Each term after the first is found by adding the common difference to the preceding term.
The calculator uses the arithmetic sequence formula:
Where:
Explanation: The formula calculates any term in the sequence by starting with the first term and adding the common difference multiplied by one less than the term number.
Details: Arithmetic sequences are fundamental in mathematics and appear in many real-world applications including financial calculations, computer science algorithms, physics problems, and more.
Tips: Enter the first term of your sequence, the common difference between terms, and the term number you want to find. All values must be valid numbers.
Q1: What if the common difference is negative?
A: The sequence will decrease by that amount each term. For example, with a=-5 and d=-3, the sequence would be -5, -8, -11, -14, etc.
Q2: Can n be a decimal or fraction?
A: In standard arithmetic sequences, n is typically a positive integer. However, the formula works mathematically for any real number n.
Q3: How is this different from geometric sequences?
A: In arithmetic sequences, terms change by addition (common difference), while in geometric sequences, terms change by multiplication (common ratio).
Q4: What's the difference between series and sequence?
A: A sequence is an ordered list of numbers, while a series is the sum of the terms of a sequence.
Q5: Can I find the sum of terms with this calculator?
A: This calculator only finds individual terms. For sum of terms, you would need a different formula (Sₙ = n/2 × (2a + (n-1)d)).