terminology
What is a sequence?
a list of numbers in a particular order
What is the recursive arithmetic formula?
an = an-1 + d
Find the next 3 terms and the common difference:
1/6, 8/21, 25/42,...
next 3 terms: 17/21, 43/42, 26/21
common difference: 3/14
Work:
8/21 - 1/6 = 3/14
25/42+3/14=17/21; 17/21+3/14=43/42; 43/42+3/14=26/21
Write an equation for the nth term for: 9, 6.5, 4,...
an = 11.5 + 2.5
Work:
6.5 - 9 = -2.5
an = 9 + (n - 1) -2.5
an = 9 - 2.5n + 2.5
an = -2.5n + 11.5
find Sn when a1 = 95, a15 = 17, and n = 15
Sn = 840
Work:
S15=15/2 (95+17) = 840
What is a term?
each number in a sequence is its own term
What is the explicit arithmetic formula?
an = a1 + (n - 1)d
Find the common difference and 10th term:
the 9th term is: 4
the 11th term is: 17
common difference: 6.5
10th term: 10.5
Work:
17-4=13;13/2 = 6.5
4+6.5 = 10.5
find the values for each variable in the formula, find a19 (look in answer)
https://docs.google.com/document/d/1rPVPOmUBS5gOynp4iVinpudzxOZdquQIE__zRM1wTy8/edit?usp=sharing (questions and answer in doc)
find S74 when n=74, a1=16, d=13
S74 = 8399
Work:
S74 = 74/2[2*16 + (16-1)13] = 8399
What is an arithmetic sequence?
a list of numbers in a particular in order in which the each term has a difference of a constant
What is the formula for an arithmetic series if you know the n, Sn, a, and d?
Sn = n/2 [2a1 + (n - 1)d]
a6 = 9 and a9 = 21:
find d and a5
d = 4
a5 = 5
Work:
21-9 = 12; 12/3 = 4
9-4 = 5
find the values for each variable in the formula, find a16 (look in answer)
https://docs.google.com/document/d/1rPVPOmUBS5gOynp4iVinpudzxOZdquQIE__zRM1wTy8/edit?usp=sharing (questions and answer in doc)
label the two formulas (look at answer)
https://docs.google.com/document/d/1rPVPOmUBS5gOynp4iVinpudzxOZdquQIE__zRM1wTy8/edit?usp=sharing (question and answer in doc)
What is the constant (the difference between two successive terms) called?
the common difference
What is the arithmetic series formula if you know n, Sn, a1, and an?
Sn = n/2 (a1 + an)
I have 14 pieces of chocolate. Every day when I go to school, I get 3 pieces taken by my friends. I also eat a piece a day. Do I have enough chocolates for my friends and I on the 4th day? How many pieces do I need for my friends and I?
No, I do not have enough pieces. I need 2 more pieces for my friends and I, then I will have enough for the day.
Work:
14-4=10; 10-4=6; 6-4=2; 2-4=-2
On the fourth day, I have two chocolates, but I am two chocolates short, meaning I need 2 more.
10, __, __, __, 334
find the missing values and identify the common difference
10, 91, 172, 253, 334
common difference: 81
Work:
334 = 10 + (5 -1) d
334 = 10 + 4d
324 = 4d
d = 81
10+81 = 91+81 = 172+253 = 334
Find the first three terms given: S43 = 13,803, n = 43, d=11
90, 101, 112
Work:
13803 = 43/2 [(2a1) + (43-1)11]
13803 = 21.5 [(2a1) + 462]
642 = 2a1 + 462
180 = 2a1
90 = a1
90+11 = 101+11 = 112
What is a series?
the sum of an arithmetic sequence
label the sigma notation (look in answer)
https://docs.google.com/document/d/1rPVPOmUBS5gOynp4iVinpudzxOZdquQIE__zRM1wTy8/edit?usp=sharing
(question and answer in the doc)
Jamie works at a bakery, she specifically makes chocolate chip cookies. Every hour she makes 26 cookies, and uses 8 chocolate chips for each cookie. Today she worked for 9 hours. Make a recursive equation to find the amount of chocolate chips she would use working 10 hours. Label each part of the equation.
a10 = a10-1 + d
2080= 1872 + 208
Work:
26*8 = 208
208*9 = 1872+208 = 2080
(the work to this problem is similar to an explicit, but the point is to know how to set up the recursive formula)
Frank has a large baseball collection that he is selling. He gets an average of more 4.678 sales a day. On his first day, though, he got 9 sales. How many sales would Frank have on his 64th day of business?
304 sales
Work:
9 + (64-1)4.678 = 303.714
Using substitution, find the sum of the terms. (look in answer)
https://docs.google.com/document/d/1rPVPOmUBS5gOynp4iVinpudzxOZdquQIE__zRM1wTy8/edit?usp=sharing (question and answer in doc)