Arithmetic sequences
An
arithmetic sequence is a sequence of numbers each of which, after the first, is obtained by adding to the preceding number a constant number called the
common difference. Thus, 3, 8, 13, 8, 23,... is an arithmetic sequence because each term is obtained by adding 5 to the preceding number.
To solve exercises using aritmetic sequences you need the following formulas:
 The nth term: a_{n}= a_{1} (n1) d
 The sum of the first n terms:
where:
a_{1} = the first term of the sequence
d = common difference (Remember you can obtain it using
d=a_{n}
a_{n1} or
.)
n = number of terms
a_{n} =
nth term
S = sum of the first
n terms
Compute the sum of the first 27 terms of the arithmetic sequence where the first terms are: 3,5,7,9,...
