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ARITHMETIC SEQUENCE
BY: LEAH V. MELENDRES
By PresenterMedia.com
• This lesson will work with arithmetic sequences, their
recursive and explicit formulas and finding terms in a
sequence. In this lesson, it is assumed that you know what
a sequence is.
Let’s look at the arithmetic sequence
20, 24, 28, 32, 36, . . .
This arithmetic sequence has a common difference of 4, meaning that we add 4 to a term in order to get the next term in the sequence.
The recursive formula for an arithmetic sequence is written in the form
an = an-1 + d
in our example, since the common difference (d) is 4, we would write:
an = an-1 + 4
So once you know the common difference in an arithmetic sequence you can write the
recursive form for that sequence. However, the recursive formula can
become diffi cult to work with if we want to find the 50th term. Using the recursive
formula, we would have to know the first 49 terms in order to find the 50 th. This
sounds like a lot of work. There must be an easier way. And there is!
• Rather than write a recursive formula, we can write an explicit formula.
Explicit formula is also sometimes called the closed form. To write the explicit or closed form of an arithmetic sequence, we use
an = a1 + (n-1)d an – is the nth term of the sequence. When writing the general
expression for an arithmetic sequence, you will not actually find a value for this. (It will be part of your much in the same way x’s and y’s are part of algebraic equations). a1 – is the first term in the sequence. n – is treated like the variable in a sequence. d – is the common difference for the arithmetic sequence. You
will either be given this value or be given enough information to it. You must substitute a value for d into the formula
•Let's Practice
1. Given an arithmetic sequence:-6, -3, 0, 3, ..., 147.What is the term number for the last number in the sequence? [a? = 147]
2. Given: 8, 6, 4, 2, ...
For the formula that represents the general term, an = dn + c, what are the correct values for d and c ?
THANK YOU!!!
