Activity 19 Review Algebra 2 Honors

Arithmetic Sequences Explicit Formula 𝑎 𝑛 = 𝑎 1 +𝑑(𝑛−1) where 𝑎 1 is the first term and d is the common difference Recursive Formula 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑

Arithmetic Sequences Practice Find the 109th term of the sequence 1, 8, 15, 22… Find the first three terms of the sequence if 𝑎 1 =−10 𝑎𝑛𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +6 The cost of admission into a waterpark is $10 plus $2 for every ride. What is the common difference in this scenario? How much does it cost to ride 12 rides? Determine whether the sequence is arithmetic. If it is, state the common difference. 20, 10, 5, … − 1 4 , − 1 2 , − 3 4 , −1,…

Arithmetic Series A series is the sum of the terms in a sequence. 𝑆 𝑛 = 𝑛 2 ( 𝑎 1 + 𝑎 𝑛 ) 𝑆 𝑛 = 𝑛 2 ( 2𝑎 1 +𝑑(𝑛−1)) Find the sum of the first 12 terms of the sequence 1, 8, 15, 22… Find the partial sum 𝑆 5 of the sequence -1, -2, -3, -4, -5 Find the partial sum 𝑆 8 of the sequence if 𝑎 1 =−10 𝑎𝑛𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +6 An auditorium has 10 seats in the first row, 11 in the second row, 12 in the third row, and so on. How many total seats are in the first 10 rows?

Sigma Notation Sigma notation is a shorthand way to write the sum of a series. Express the following sum using sigma notation. 2+8+14+20+26+32 Find the indicated partial sum 𝑛=1 13 2𝑛