Algebra I Unit 10: Arithmetic & Geometric Sequences
For each of the following sequences, determine if they are arithmetic or not. If they are an arithmetic sequence, determine the common difference. If they are not an arithmetic sequence, state why they do not classify.
Sequence
{35,32,29,26,...} {−3, −23, −43, −63, ... } {1,2,4,8,16,...} {−7, −9, −11, −13, ... } {9,14,19,24,...}
Arithmetic Sequence Formulas
Arithmetic?
Common Difference
1st Term
7th Term
An equation that can be used to find the h term of the sequence is called the _________________________. An equation that can used to find a term if the previous term is known is called _________________________.
Explicit Formula
Recursive Formula
= +(−) = ________________________
= ___________________________
= ___________________________
*Can be used to find any term.
Let’s practice writing these formulas:
Sequence
{1,5,9,13,17,...} {9,7,5,3,1,...} {15,30,45,60,75,...}
= −1 + = ________________________
Where...
Where...
−1 = ___________________________
= ___________________________
*Can be used to find a term if the previous term is known.
Explicit form
Recursive form
*Most explicit forms you will deal with will be simplified and will look like _____________ format. Practice getting the first explicit form in the table in = + format.