Finding the sum of the first term and common difference when given sum of first 5 and sum of first 10 the sum of the first 5 terms of an arithmetic series is 110 and the sum of the first 10 terms is 320. How do i go about finding the first term and common difference.
Sn  = n/2 [2a+d(n−1)] is the equation for working out the sum of an arithmetic series, but how can i rearrange to find for the first term and common difference. I belive it would be using simulatenous equations.

Let first term $a_1$ be A (for ease of writing):
$$s_n=\frac{n}{2}[2A+(n-1)d]$$
Since $S_5=110$
$$s_5=110=\frac{5}{2}[2A+(5-1)d]$$
$$44=2A+4d \tag1$$
Since $S_{10}=320$
$$s_{10}=320=\frac{10}{2}[2A+(10-1)d]$$
$$64=2A+9d\tag2$$
Solving (1) and (2), We get:
$$d=4$$
Using either (1) or (2), say (1), we substitute $d=4$ to get $A$:
$$44=2A+4(4)$$
Solving for $A$, we get $$A=14$$
The series is:
$$14, 18, 22, 26, 30, 34, 38, 42, 46, 50, ...$$
Note: Arithmatic Progression-Wiki has a good list of formulae related to this subject.
