Page 16 - Math SL HB Sem 1
P. 16
SEOIJENCE AND EzuES
ARITHMETIC SEQUENCE (oT ARITHMETIC PRoGRxSsIoN)
Definition:
A sequence \,u2,u1,...,u1 is called an arithmetic sequence ( or progression), ifthere
exists a constantd, called the common difference, such that
d,: un un_., for every n > I
-
If u } is an arithmetic sequence with common difference, d, then we write the
{
"
sequence ut,u2,ut,--.,u,,.-.'u, as
ul \ *d, ut+2d,..., z, +(i-l)d a, +(n-l)d
J J J
First term j" term n* term
The n'/' term is u, = u, + (n l
- )d
Example I : Whi ch of the lollowing is an arithmctic sequence?
(a) t ,2,3 ,5,... (b) 3,3,3,3...
Example2: The 8th term ofan arithmetic progression is ll andthe.l5,, term is2l. Find
the common difference, the first term of the series and then nth term.
