Dynamic Activity

Arithmetic Sequences

Lesson Vocabulary

• arithmetic sequence
• common difference
• arithmetic mean

Take Note Key Concept: Arithmetic Sequence

An arithmetic sequence with a starting value a and common difference d is a sequence of the form

a , a + d , a + 2 d , a + 3 d , … eh comma eh plus d comma eh plus 2 d comma eh plus 3 d comma dot dot dot

A recursive definition for this sequence has two parts:

a 1 = a initial condition a n = a n − 1 + d ,   for   n > 1 recursive formula table with 2 rows and 3 columns , row1 column 1 , eh sub 1 , column 2 equals eh , column 3 initialcondition , row2 column 1 , eh sub n , column 2 equals . eh sub n minus 1 end sub . plus d comma for n greater than 1 , column 3 recursiveformula , end table

An explicit definition for this sequence is a single formula:

a n = a + ( n − 1 ) d , for  n ≥ 1 eh sub n , equals eh plus open n minus 1 close d comma , for , n greater than or equal to 1