In an Arithmetic Sequence the difference between one term and the next is a constant.

In General we could write an arithmetic sequence like this:

{at, t+d, t+2d, t+3d, … }

where:

t is the first term, and

d is the difference between the terms (called the “common difference”)

Example : My Arithmetic Sequences : 11,2,-7,-16,-25,-34

Know :

– t = 11 (the first term)

– d = -9 (the “common difference” between terms)

We can write an Arithmetic Sequence as a formula :

= t1+(n-1).d

Using the Arithmetic Sequence formula:

=t1+(n-1).d

=11+(n-1).(-9)

-34=11+9-9n

-34=20-9n

n=(6)

Example 2 : I want to determine t50

I know : t1= 11

n=50

n-1=50-1=49

Using the Arithmetic Sequence Rule :

= t1+49.d

= 11+49.(-9)

= -430

To sum up the terms of this arithmetic sequence:

t1 + (t2+d) + (t3+2d) + (t4+3d) + …

Use this formula:

Example: Determine the sum of this Arithmetic Sequence : 11,2,-7,-16,-25,-34

The values of t,d and n are:

t = 11 (the first term)

d = -9 (the “common difference” between terms)

n (how many terms to add up)