Section 9.2 Arithmetic Sequences and Partial Sums

A sequence whose consecutive terms have a common difference is called an arithmetic sequence





Definition of Arithmetic Sequence

A sequence is arithmetic if the differences between consecutive terms are the same. So, the sequence

is arithmetic if there is a number d such that

The number d is the common difference of the arithmetic sequence

The nth Term of an Arithmetic Sequence



The nth term of an arithmetic sequence has the form



a_n = dn + c




where d is the common difference between consecutive terms of the sequence and c = a_1 - d





The Sum of a Finite Arithmetic Sequence




The sum of a finite arithmetic sequence with n terms is



S_n = (n/2)(a_1 + a_n).



Example:



Find the sum of of the integers from 1 to 100



S_n = 1+2+3+4+5+6+...+99+100


= (n/2)(a_1 + a_n)


= (100/2)(1+100)


= 50(101)


=5050