Arithmetic Sequences

An arithmetic sequence is a sequence where the first term is a and the difference between consecutive terms is constant and is called d.

For example , if the first term a =11, d=3, the nth term= 11+ 3 (n-1)= 3n+8

11,14,17,20,23, ....

a=1, d=-1/2 , nth term= 1+ (n-1)-0.5=0.5-0.5n

0, -0.5,-1,-1.5, -2....

The 9th term of an arithmetic sequence is 3 and the 11th of the sequence is -4

Deduce a and d.

3=a+8d (1)

-4= a+10d (2)

(1) -(2) :7= -2d , d=-3.5 and a= -4+35=31