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Unit 8 Sequences and – Arithmetic Sequences and Series Notes

Objective 1: Be able to recognize and write the rules for arithmetic sequences, including finding the common difference, finding the nth term, and finding the of terms of a given sequence.

Examples of arithmetic sequences:

3, 7, 11, 15, 19, …

-1, 5, 11, 17, 23, …

37, 28, 19, 10, …

Note: all arithmetic sequences have a ______.

A rule (formula) can be written to find the nth term of an arithmetic sequence.

an  a1  dn 1

Write the general rule and find a20 for each of the following sequences.

11, 14, 17, 20, 23, …

-8, -1, 6, 13, 20, 27, …

Find the first 5 terms of the sequence an  2n3 and graph them. a1 = a2 = a3 = a4 = a5 =

Note: the graph is a set of discrete values with the domain being the set of positive . While it is a linear pattern, it is NOT a line! Write the rule for the arithmetic sequence given the 5th term of a sequence is 24 and the common difference is 6.

Write the rule for the arithmetic sequence given the 7th term of a sequence is 41 and the common difference is -3.

Write the rule for the arithmetic sequence given the 3rd term is 17 and the 9th term is 47.

Write the rule for the arithmetic sequence given the 12th term is 32 and the 16th term is 56.

Find the number of terms in the sequence: 8, 15, 22, 29, …288.

Find the number of terms in the sequence: 11, 19, 27, 35, …211.

Objective 2: Be able to find the sum of an arithmetic series, evaluate using notation – including within applications.

Find the sum of 1 + 2 + 3 + 4 + … + 17 + 18 + 19 + 20

The formula to find the sum of an arithmetic sequences is Sn 

Use the formula to find the sum of the first 50 terms of the given series.

5 + 12 + 19 + 26 + …

50 + 42 + 34 + 26 + …

Evaluate:

100 50 6n 5 2n34 n1 n1

Determine the number of terms in the series.

4 + 7 + 10 + 13 + 16 … Sn = 175

1. A theater has 25 seats in the first row and one additional seat in each successive row. The theater has 80 rows. a) How many seats are there in row 50?

b) How many total seats are there in the theater?

2. An employee has a starting salary of \$40,000 and will get a \$3000 raise every year for the first 10 years. a) How much will the employee make in year 6?

b) What will the employees total earned income over the 10 years?

3. A corner section of a stadium has 8 seats along the front row. Each successive row has two more seats than the row preceding. If the top row has 24 seats, how many seats are in the entire section?

4. Given 푎1 = 4 and 푎푛 = 푎푛−1 + 3, write the explicit formula. (from Common Core Flipbook)