Honors Pre-Calculus A, 3rd Hour, Winter 2016: 9.2 Arithmetic Sequences and Partial Sums

9.2 Arithmetic Sequences and Partial Sums

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

The sequence

          $a_{1},a_{2},a_{3},a_{4},...,a_{n},...$
is arithmetic if there is a number d such that

         $a_{2}-a_{1}=a_{3}- a_{2}=a_{4}-a_{3}=...=d$

The number d is the common difference of the arithmetic sequence

Ex.

$7,11,15,19,...,4n+3,...$

$11-7=4$
$15-11=4$
$19-15=4$

$d=4$

$2,-3,-8,-13,...,7-5n,...$

$-3-2=-5$
$-8-(-3)=-5$
$-13-(-8)=-5$

$d=-5$

The nth term of an arithmetic sequence has the form

$a_{n}=a_{1}+d(n-1)$

where d is the common difference between consecutive terms of the sequence

Ex.

Find a formula for the nth term of the arithmetic sequence whose common difference is 3 and whose first term is 2.

$a_{n}=a_{1}+d(n-1)$

$d=3$
$a_{1}=2$
$n=?$

Therefore,

$a_{n}=2+3(n-1)$

Find the 6th term of the above sequence.

$d=3$
$a_{1}=2$
$n=6$

$a_{6}=2+3(6-1)$
$a_{6}=2+3(5)$
$a_{6}=2+15$
$a_{6}=17$

The sum of a finite arithmetic sequence with n terms is

$S_{n}=\frac{n}{2}(a_{1}+a_{n})$

Find the sum of the integers from 1 to 100

$S_{n}=\frac{n}{2}(a_{1}+a_{n})$

$a_{1}=1$
$a_{n}=100$
$n=100$

$S_{100}=\frac{100}{2}(1+100)$
$S_{100}=50(101)$

$S_{100}=5050$

Honors Pre-Calculus A, 3rd Hour, Winter 2016

Tuesday, May 10, 2016

9.2 Arithmetic Sequences and Partial Sums

9.2 Arithmetic Sequences and Partial Sums

No comments:

Post a Comment