11.2 Homework:
11.2a and 11.2b on Math XL
11.2: Arithmetic Sequences
Observe the following sequences:
i.
ii.
iii.
4, 9, 14, 19, 24, …
2, 0, −2, −4, −6, …
√2, √2 + 𝜋, √2 + 2𝜋, √2 + 3𝜋, …
What do they all have in common?
In the above examples, the common differences are 5, -2, and 𝜋
respectively.
1.
Write the first 6 terms of each arithmetic sequence.
a) 𝑎1 = 5, 𝑑 = 6
1
b)
𝑎1 = −2, 𝑑 =
c)
𝑎1 = 16, 𝑎𝑛 = 𝑎𝑛−1 − 1.5
2
Let’s generalize a formula for the nth term of an arithmetic sequence
given a first term 𝑎1 and a common difference d.
𝒂𝟏 = 𝒂𝟏
𝒂𝟐 = 𝒂𝟏 + 𝒅
𝒂𝟑 = 𝑎2 + 𝑑 = 𝑎1 + 𝑑 + 𝑑 = 𝒂𝟏 + 𝟐𝒅
𝒂𝟒 = 𝑎3 + 𝑑 = 𝑎1 + 2𝑑 + 𝑑 = 𝒂𝟏 + 𝟑𝒅
𝒂𝟓 = 𝑎4 + 𝑑 = 𝑎1 + 3𝑑 + 𝑑 = 𝒂𝟏 + 𝟒𝒅
See the pattern?
2.
Find the general term (the nth term) of the sequence such that
𝑎1 = 6 and 𝑑 = −8.
3.
Find 𝑎31 when 𝑎1 = −4, 𝑑 = .
5
2
4.
𝑎10 = 27 and 𝑎41 = 151. Find the first term and the common
difference. (Hint: set up a system).
5.
Write a formula for the general term (the nth term) of the
sequence: 𝑎1 = 6, 𝑎𝑛 = 𝑎𝑛−1 − 12
Sum of the first n terms of an arithmetic sequence
The sum of the first n terms of an arithmetic sequence, denoted 𝑆𝑛 , is
called the nth partial sum of the sequence:
𝑆𝑛 = 𝑎1 + 𝑎2 + ⋯ + 𝑎𝑛
Let’s derive a formula for 𝑆𝑛 :
6.
Find the sum of the first 30 terms of the arithmetic sequence:
−19, −12, −5, …
7.
Find the sum of all integers divisible by 3 between 18 and 51.
8.
Find (in terms of n): 1 + 2 + 3 + ⋯ + 𝑛
9.
Find:
37
∑(3𝑖 − 4)
𝑖=1
10.
Find (in terms of n):
𝑛
∑(4𝑖 + 2)
𝑖=1
11.
Mr. Cawelti has an army of Pikmin that increases every day. On
day 1 he has 1 Pikmin. On day 2, he acquires 3 more. On day 3, he
acquires 5 more. If this trend continues, when should he expect to
have 10,000 Pikmin?
https://www.youtube.com/watch?v=w-I6XTVZXww