Writing a General Formula of an Arithmetic Sequence

This algebra video tutorial explains how to write a general formula of an arithmetic sequence. It explains how to see the patterns in to the write a general equation for the sequence. Most of the sequences are arithmetic sequences. Examples include fractions and terms with alternating signs. This video provides the general formula for the nth term of an arithmetic sequence. This tutorial contains plenty of examples and practice problems.

Algebra For Beginners:

Arithmetic Sequences and Series:

Sigma Notation and Summation:

Writing a General Formula of an Arithmetic Sequence:

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Recursive Formulas:

Fibonacci Sequence:

Geometric Sequences and Series:

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Sequences - Free Formula Sheet:

Algebra and Precalculus Videos:

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[akiotakahashisan]

My teacher said to just guess the general rule...but I don't like guessing things...I like following formulas...so thanks for getting a formula to GET the formula hahahah...but the negative, positive, negative, positive sequences are the ones that I am worried about but I think I got this...thanks again.

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[noahsibahi-jackson]

An alternative method for an equation to solve for a sequence's equation is by writing a(n)=d(n)+a(0)
[()=subscript], whereby a(n)= the sequence and or the coefficient as the common difference number times an interchangeable number [n], + the sequence to a subscript of 0 [a(0)] given this is equal to the constant that upscales or downscales each term [i.e 7, 10, 13 and 3, 6, 9 are technically both the same sequence only the constant of a(0) is different with it being 4 for the first variation and 0 for the second variation] depending on the sign of its value (positive or negative) given a subscript 0 is also a value that differentiates a variation of sequence from an original sequence that is otherwise identical and is a value that exists independently of the common difference between numbers. This way the equation can be applied to any type of arithmetic sequence regardless of its values and conditions as you simply have to substitute numbers into this skeleton or outline, while this is technically accomplishing the same result it is easier to remember this formula and it is more universal.

Additional formulas and summary: d=a(2)-a(1)
a(0)=a1-d=a(1)-[a(2)-a(1)]
a(n)=d(n)+a(0)

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