Stefen McCone
An arithmetic sequence is a sequence with the difference between two consecutive terms. Also called the common difference.




Arithmetic Sequences:


What is an arithmetic sequence?
An arithmetic sequence is a sequence that has a constant generator that is either addition or subtraction.

What does its graph look like?
Its graph is a linear. Because it is a discrete function, you should not connect the points.

What is the equation?
Initial Term+ (Generator x Input of Term You Are Solving For)= Output

What do the terms look like?
The terms have a constant difference such as: 5, 10, 15, 20, 25…

What do the staircases mean?
When graphed the staircases of an arithmetic sequence are all the same, they stand for the generator.

What does the initial value mean?
The initial value, or first value of the sequence, is the y-intercept.



Marjorie Moreno:
An arithmetic sequence is created by adding a constant number to a term to generate the next term
In other words, arithmetic sequence is a sequence of numbers in which each term except the first term is the result of adding the same number, called the common difference, to the preceding term.
The sequence 5, 11, 17, 23, 29, 35 . . . is an arithmetic sequence, because the same number 6 (the common difference) is added to each term of the sequence to get the succeeding term.
Arithmetic series is the indicated sum of the terms of an arithmetic sequence.

  • The sequence 5, 11, 17, 23, 29, 35 is an arithmetic sequence.
5 + 11 + 17 + 23 + 29 + 35 is the corresponding arithmetic series.

practice:
Find the next four terms of the given arithmetic sequence.
7, 4, 1, - 2, - 5 . .
Choices:
A. – 3, - 3, - 3, - 3
B. – 8, -5, -2, 1
C. – 8, - 11, - 14, - 17
D. 8, 11, 14, 17

Correct Answer: C
Solution:
Step 1: The common difference for the given sequence is – 3.
Step 2: So, the next four terms are – 8, - 11, - 14, - 17.