Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

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Presentation transcript:

Unit 9: Sequences and Series

Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an infinite sequence Each # in a sequence is called a term Ex. 3, 5, 7, 9…. a 1 =3 a 2 =5

Arithmetic Sequences 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 Ex. Find the common difference (one term minus the previous term) 55, 49, 43, 37, 31, 25,19

Is the sequence arithmetic? If so give the common difference. -4, -1, 2, 5, 8…… 7, 3, -1, -5, -9…… 3, 6, 12, 24…… 3, 8

Use the recursive formula to find the first four terms of the arithmetic sequence given.

Use the recursive formula to write the first four terms of the arithmetic sequence.

List the first three terms of the arithmetic sequence.

Another one...

Let’s figure out the explicit formula. 1 st Term: 2 nd Term: 3 rd Term: 4 th Term: 10 th Term: nth Term:

Arithmetic Sequences Formula for the general pattern for any arithmetic sequence:

Arithmetic Sequences Write a equation for the n th term of the following sequence

Arithmetic Sequences

Find a 15

Arithmetic Sequences In the sequence below, which term has a value of 286?

Arithmetic Sequences What is the value of the first term if the 9 th and 10 th terms are 4 and 2 consecutively?

Arithmetic Sequences If the 3 rd term of an arithmetic sequence is 8 and the 16 th term is 47, find a 1 and d

Arithmetic Means Terms between any two non-successive terms of an arithmetic sequence Find 4 arithmetic means between 16 and 91

Arithmetic Means Find 1 arithmetic mean between 50 and -120

Arithmetic Series A series is the indicated sum of the terms of a sequence If the seq. is 18, 22, 26, 30 The arith series is

Arithmetic Series To find the sum of an arithmetic series,

Arithmetic Series Find the sum of the first 100 positive integers.

Arithmetic Series Find the sum of the first 20 even numbers beginning with 2.

Arithmetic Series Find the sum of …+2

Arithmetic Series Find the sum of …+97