1. 8.2 – Arithmetic Sequences

2. A sequence is arithmetic if the difference between consecutive terms is constant Ex: 3, 7, 11, 15, … The formula for arithmetic sequences is a n = d(n – 1) + a 1 d = the common difference between successive terms Can also use a n = nd + a 0 Write your final answer in linear form (like y = mx+b) Ex: Write a formula for the sequence -4, 3, 10, 17, … a 1 = -4, d = 7 a n = 7(n – 1) – 4 a n = 7n – 7 – 4 a n = 7n - 11

3. The sum of a finite arithmetic sequence is: n = # terms being summed a 1 = 1 st term being summed, a n = last term being summed Infinite arithmetic sequences cannot be summed Ex: Find the sum of the first 100 natural numbers. n = 100, a 1 = 1, a 100 = 100 Carl Friedrich Gauss derived this formula in 2 nd grade!

4. Ex: Find the sum of the first 38 terms of the sequence: 167, 151, 135, 119, … a 1 = 167, d = -16, but what’s a 38 ? a 38 = -16(38 – 1) + 167 a 38 = -425

5. A stack of soup cans has 28 cans on the bottom, 27 cans on the 2 nd row, 26 on the 3 rd row, etc. How many cans are there in the first 21 rows? 1. 231 2. 370 3. 332 4. 196 5. 378

6. Find the sum of the 13 th through the 28 th terms of the following sequence: 4, 7, 10, 13, … 1. 968 2. 1296 3. 937.5 4. 1000 5. 360