Arithmetic Sequences and Partial Sums

Definition of an Arithmetic Sequence - a sequence whose consecutive terms have a common difference

The common difference (d) is the difference between two consecutive numbers in the sequence.

Example:

4, 8, 11, 14, 17,...

d=3

You can find the nth term of an Arithmetic Sequence by using the equation...

an = dn + c

where c = a1 -d

The equation can also be written as an = d(n-1) + a1

Example:

2, 6, 10, 14, 18

d=4

c=2

an = 4n - 2

The equation for the Sum of a Finite Arithmetic Sequence...

Sn = (n/2)(a1 + an)

You can use this equation to add up the numbers in a Arithmetic Sequence.

Example:

Sn = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +.....+ 98 + 99 + 100

= (100/2)(1 + 100)
= 50(101)
=5050

You can find a Partial Sum of an Arithmetic Sequence by using the equation for the Sum of a Finite Arithmetic Sequence.

Example:

5, 16, 27, 38, 49,....
Find the 150th term

an = dn + c
a150 = 11(150) - 6
a150 = 1644

S150 = (150/2)(5 + 1644)
S150 = 75(1649)
S150 = 123,675