1. Ch. 8 – Sequences, Series, and Probability
8.2 – Arithmetic Sequences

2. The formula for arithmetic sequences is an = d(n – 1) + a1
A sequence is arithmetic if the difference between consecutive terms is constant
Ex: 3, 7, 11, 15, …
The formula for arithmetic sequences is an = d(n – 1) + a1
d = the common difference between successive terms
Can also use an = nd + a0
Write your final answer in linear form (like y = mx+b)
Ex: Write a formula for the sequence -4, 3, 10, 17, …
a1 = -4, d = 7
an = 7(n – 1) – 4
an = 7n – 7 – 4
an = 7n - 11

3. The sum of a finite arithmetic sequence is:
n = # terms being summed
a1 = 1st term being summed, an = last term being summed
Infinite arithmetic sequences cannot be summed
Ex: Find the sum of the first 100 natural numbers.
n = 100, a1 = 1, a100 = 100
Carl Friedrich Gauss derived this formula in 2nd grade!

4. Ex: Find the sum of the first 38 terms of the sequence:
167, 151, 135, 119, …
a1 = 167, d = -16, but what’s a38?
a38 = -16(38 – 1) + 167
a38 = -425

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

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