13.1 – Finite Sequences and Series

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Presentation transcript:

13.1 – Finite Sequences and Series Essential Question: What is the difference between an arithmetic and a geometric sequence?

Vocabulary Sequence – a set of #’s or terms arranged in a particular order. Arithmetic Sequence – the difference of any 2 consecutive terms is constant. (common difference, + or – ) When you add the same number to each term. (NOTE: you can add a negative which looks like subtraction.)

Vocab. Geometric Sequence – the ratio of any 2 consecutive terms is constant. (common ratio, × or ÷ ) When you multiply each term by the same number. (NOTE: you can multiply by a rational number as well as a whole number.)

We use the notation to talk about the “n”th term. Formulas for the “n”th term are as follows:

Arithmetic Sequence Common Difference To get the “n”th term The “n” term 1st term

Geometric Sequence The “n” term To get the “n”th term Common Ratio 1st term

Example Find a formula for tn and sketch the graph. 1, 4, 7, 10, … 8, 4, 2, 1, …

Example State whether the given sequence is arithmetic, geometric, or neither. Find a formula for tn in terms of n, and evaluate t8. a. b. c. 15, 11, 7, 3, …

Example In a certain sequence, t2 = 2 and t5 = 16. Find t10 if the sequence is: arithmetic geometric

Example Find the # of multiples of 7 between 30 and 300.