What is an Arithmetic Sequence?
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DEF: If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence.
• The number added to each term is constant (always the same). • The fixed amount is called the common difference, d. To find the common difference, subtract the first term from the second term.
Find the common difference, d, and the next two terms in each of the arithmetic sequences.
1) 1, 4, 7, 10, 13, 16, ...
2) 15, 10, 5, 0, ­5, ­10, ...
3) 4) Find the common difference for the arithmetic sequence whose formula is an = 6n + 3
Formula used to find a specific term in an arithmetic sequence: Ex. ­3, ­1, 1, 3, 5, ...
a. Is this an arithmetic sequence?
b. What is the common difference?
c. What is the 12th term?
d. What is the 20th term?
e. What is an?
5) Find the 10th term of the sequence 3, 5, 7, 9, ...
6) For a certain arithmetic sequence, a1=2 and a2=9. Find the 9th term. 7) Find the number of terms in the sequence 7, 10, 13, ..., 55.
Formula used to find the sum of an arithmetic sequences:
8) Find the sum of the first 12 positive even integers.
9) A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern. If the theater has 20 rows of seats, a) Find how many seats are in the 20th row?
b) Find how many seats are in the theater?
Groupwork:
1) Find the 25th term of the sequence ­7, ­4, ­1, 2, ...
2) Find a7 for an arithmetic sequence where a1 = 3x and d = ­x. 3) Find the sum of the first 25 terms of the arithmetic series 2, 8, 14, 20,......
Homework:
1) Determine if the sequence is arithmetic, if so state the common difference
5, 9, 13, 17 ...
2) Find the 12th term for this arithmetic sequence 5, 9, 13, 17 ...
3) Find the sum of the first 20 terms of the sequence 4, 6, 8, 10, ...
4) Find the sum of the sequence ­8, ­5, ­2, ..., 7
5) Find a6 for an arithmetic sequence where a1 = 3x+1 and d = 2x+6.
6) A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans. How many cans, in total, are in the display?
7. Find the 10th term:
a) 11, 14, 17, 20, ... b) 20, 17, 14, 11, ...