Page 16 - Math SL HB Sem 1

srioTJENCE AND SERIES

ARITIIMFI,TIC SEQtiENCE (or ARITHME'IIC PROGRESSTON)

Definition:

A sequence ut,tt2,t\,...,u,1 is called an arithmetic sequence ( or progression), ifthere
exists a constantd, called the common difference, such that
d= u,-u,, lor every n > I

If u } is an arithmetic sequence with common difference, d, then we write the
{
"
sequence ut,u 1,u1,...,u,, --.,u as
n
\, q+d' u,+2d, , a, +(i- l)d a, +(n- l)d
J J J

First term i'h lerm nk lerm

The n'r' term is u, - u, + (n - )d
I

Examplel : Which of the lollowing is an arithmetic sequence?
(a) 1,2,3,5,... (b) 3,3,3,3,...

Example2: The 8rh term ofan arithmetic progression is ll andthe.l5'' term is 21. Find
the common difference, the first term of the series and then nth term.

.\A