Arithmetic Sequence & Series Practice 1. An arithmetic sequence is defined by 𝑢𝑛 = a. b. c. d. e. 1+3𝑛 2 where n is a positive integer. Find 𝑢1 and 𝑢2 . Write down the common difference. Find 𝑢21 . Find the first term of the sequence that is greater than 45. Use your graphic display calculator to find the sum of the first 90 terms of 𝑢𝑛 . 2. The 𝑛𝑡ℎ term of a sequence is 𝑎𝑛 = 3𝑛(𝑛 + 1) where n is a positive integer. a. Write down the values 𝑎1 , 𝑎2 , and 𝑎3 . b. Show that the sequence is not arithmetic. 3. Find the common difference d and the first term 𝑢1 of an arithmetic sequence given that 𝑢3 = 12 and 𝑢7 = 20. 4. Find the common difference d and the first term 𝑢1 of an arithmetic sequence given that 𝑢6 = −4 and 𝑢10 = −12. 5. Calculate the sum of the first 30 multiples of 4. 6. The cost of renting a motorcycle is $30 for the first hour and $8 for each additional hour. a. Write down the cost of renting the motorcycle for i. 2 hours ii. 3 hours b. Calculate the cost of renting the motorcycle for 12 hours. The motorcycle can be rented daily for a special rate of $160 per day. c. Calculate the least number of hours that the motorcycle must be rented so that the special rate is cheaper. 7. The sequence 3, a, 10, b … is arithmetic. a. Find the value of a. b. Write down the common difference. c. Find b. d. Find the 11th term. 8. Three consecutive terms of an arithmetic sequence are 3𝑘 + 1, 3 + 4𝑘, and 7𝑘 − 1. a. Find k. b. Write down the values of these three terms. 9. In the arithmetic sequence 𝑢1 , 𝑢2 , 𝑢3 , … it is known that 𝑆1 = 5 𝑎𝑛𝑑 𝑆2 = 12. a. Write down i. 𝑢1 ii. 𝑢2 b. Find the common difference, d. c. Find 𝑆4 . 10. In the following statements 𝑢𝑛 is an arithmetic sequence with common difference 𝑑. Decide whether or not these statements are true: a. 𝑑 = 𝑢7 − 𝑢6 b. 𝑢12 = 𝑢3 + 9𝑑 c. 𝑢6 = 2𝑢3 d. 𝑆25 = 𝑆24 + 𝑢24 e. 𝑆10 = 5(𝑢1 + 𝑢10 )