Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.

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Presentation transcript:

Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.

Arithmetic Sequences Sequence: a list of numbers in a specific order. Term: each number in a sequence

Arithmetic Sequences Arithmetic Sequence: a sequence in which each term after the first term is found by adding a constant, called the common difference (d), to the previous term. Common Difference : refers to the difference between a given term and the next term in an arithmetic sequence.

Find the Common Difference 82, 76, 70, 64 What is the common difference of the arithmetic sequence? Find the next 3 terms in the sequence. 82, 76, 70, 64, -6 58,52,46

Recursive Form Use the recursive form to find the next term or the next few terms in an arithmetic sequence. t n = t n-1 + d d = the common difference n = the term you are wanting to find Find the next term of the following arithmetic sequence using the formula above. 3, 6, 9, 12

Closed Form Use the closed formula to find the n th term of an arithmetic sequence. a n = a 1 + (n – 1)d n = the term you are wanting to find a 1 = the first term of the sequence d = the common difference Find the 201 st term of the following sequence using the formula above: 82, 76, 70, 64 a 201 = 82 + (201 – 1)(-6) a 201 = -1118