Formula For A Sequence
Formula For A Sequence is a Grade 8 algebra skill in Saxon Math Course 3, Chapter 7, where students write and use general term formulas to find any term in an arithmetic or geometric sequence. Writing a formula from a pattern is a key algebraic thinking skill that prepares students for function notation and higher-level algebra.
Key Concepts
Property A formula relates the value of a term ($a$) with its number ($n$). For the sequence $3, 6, 9, \dots$, the formula is $a n = 3n$.
Examples For an arithmetic sequence $5, 10, 15, \dots$, the formula is $a n=5n$. The 20th term is $a {20}=5(20)=100$. For a geometric sequence $2, 4, 8, \dots$, the formula is $a n=2^n$. The 6th term is $a 6 = 2^6 = 64$. Using the formula $a n = n+5$, the first three terms are $a 1=1+5=6$, $a 2=2+5=7$, and $a 3=3+5=8$.
Explanation A formula is like a secret code that helps you find any term in a sequence without listing them all. Just plug in the term's position number ($n$), and the recipe instantly gives you its value ($a n$). This is a massive shortcut, especially if you need to find the 100th term without doing 99 calculations first!
Common Questions
What is the general term formula for a sequence?
The general term formula expresses the value of the nth term of a sequence as a function of n. For an arithmetic sequence: a_n = a_1 + (n-1)d. For a geometric sequence: a_n = a_1 times r to the power of (n-1).
How do you write a formula for an arithmetic sequence?
Identify the first term a_1 and the common difference d, then write a_n = a_1 + (n-1)d. For example, for the sequence 5, 8, 11, the formula is a_n = 5 + (n-1) times 3.
How do you use a sequence formula to find a specific term?
Substitute the term position n into the formula and simplify. For example, to find the 10th term of a_n = 5 + (n-1) times 3, substitute n = 10: a_10 = 5 + 9 times 3 = 32.
How do you write a formula for a geometric sequence?
Identify the first term a_1 and the common ratio r, then write a_n = a_1 times r to the power (n-1). For the sequence 2, 6, 18, the formula is a_n = 2 times 3 to the power (n-1).
Where is writing formulas for sequences taught in Grade 8?
This skill is covered in Saxon Math Course 3, Chapter 7: Algebra.