ARITHMETIC SEQUENCES AND SERIES

1. ARITHMETIC SEQUENCES AND SERIES WORD PROBLEMS EQ1 - Is it a sequence value or a sum?

2. Example 1: Sequence • The purchase of an office computer is $12500. Its annual depreciation is $1875. Find the value of the computer after 6 years of depreciation. a0=12500 d = -1875 an= 12500 + (n-1)(-1875) when n = 6 a6= 12500 + (6)(-1875) = $1250

3. Example 2: Series • A man gets a job with a salary of $30000 a year. He is promised a $2300 raise each subsequent year. Find his total earnings for a 10-year period. an = 30000 + (n-1)(2300) Salary in the beginning of the 10th year. a10 = 30000 + (10 – 1)(2300) = $50700 Sum of first 10-year salaries: S10 = 5(30000 + 50700) = $403500

4. Example 3: Sequence • On November 1 an English teacher had his class read five pages of a long novel. He then told them to increase their daily reading by three pages each day. Write a formula for the number of pages that they will read on the nth day of November. If they follow the teacher’s instructions, then how many pages will they be reading on the last day of November?

5. Example 4: Series • A grocer wants to build a “mountain” out of cans of mountain-grown coffee. The first level is to be a rectangle containing 9 rows of 12 cans in each row. Each level after the first is to contain one less row with 12 cans in each row. Finally, the top level is to contain one row of 12 cans. • Write a sequence whose terms are the number of cans at each level. an = 108 + (n – 1)-12

6. Example 4: continued • Write the sum of the terms of this sequence in summation notation and find the total number of cans in the mountain.