Section 4-7: Arithmetic Sequences.

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Presentation transcript:

Section 4-7: Arithmetic Sequences

A sequence in which a constant d can be added to each term to get the next term is called an Arithmetic Sequence. The constant d is called the Definition: Common Difference. To find the common difference (d), subtract any term from one that follows it. 2 5 8 11 14 3 3 3 3

Find the first term and the common difference of each arithmetic sequence. Examples: First term: 4 Common difference (d): = 9 – 4 = 5 First term: 34 Common difference (d): -7 BE CAREFUL: ALWAYS CHECK TO MAKE SURE THE DIFFERENCE IS THE SAME BETWEEN EACH TERM !

The first term of an arithmetic sequence is The first term of an arithmetic sequence is . We add d to get the next term. There is a pattern, therefore there is a formula we can use to give use any term that we need without listing the whole sequence . The nth term of an arithmetic sequence is given by: The last # in the sequence/or the # you are looking for The position the term is in First term The common difference

Examples: Find the 14th term of the arithmetic sequence 4, 7, 10, 13,……

Examples: In the arithmetic sequence 4,7,10,13,…, which term has a value of 301?