Arithmetic Series
A
series such as 3 + 7 + 11 +
15 + ··· +
99 or 10 + 20 + 30 + ··· + 1000 which
has a constant difference between terms.
The first term is a_{1}, the common difference
is d,
and the number of terms is n. The sum of
an arithmetic series is found by multiplying the number of
terms times
the average of the first and last terms.
Formula: 
or 


Example: 
3 + 7 + 11 + 15 + ··· + 99 has a_{1} = 3 and d = 4. To find n, use the explicit formula for an arithmetic sequence.
We solve 3 + (n – 1)·4 = 99 to get n = 25.
or

See
also
Geometric
series
