# Find $v$, $a_1$ or $a_n$ in an arithmetic series

Following Data are given in an arithmetic series: S$_{25}$=1275 (and so n = 25)

When trying to find other elements of the formulas I have learned so far:

1. $a_n = a_1 + (n-1)v$
2. $s_n = n \cdot ((a_1 + a_n)/2)$

I came to the conclusion that $a_1+a_n$ should equal 102 but I can't seem to find a specific value for $a_1$, $a_n$ or $v$. I also found that $a_1$ should equal $-6v + 25,5$.

Can someone give me a hint or just a few steps towards the solution because to me it looks like I am stuck with $3$ unknown factors.

(Symbols: $a_1$ means the first term and so $a_n$ means the $n$-th term, $s_n$ is the sum of the first $n$ terms and $v$ is the difference between $2$ terms following each other)

• Remember that not all studiy the same and in the same place: explain your symbols. – DonAntonio May 31 '16 at 15:29
• @Joanpemo, i tried to explain the used symbols in my best English, i hope you understand. – Michelle_B May 31 '16 at 15:45
• Thank you. Then, as noted in Schrodinger's answer, there is no one unique answer but infinite many. – DonAntonio May 31 '16 at 17:07
• I think I indeed interpreted the question in my textbook wrong, I hope to give an update on this problem soon ^^ – Michelle_B May 31 '16 at 17:18
• The number $v = a_{k + 1} - a_k$ for each positive integer $k$ is called the common difference. – N. F. Taussig Jun 1 '16 at 11:44

You have $2$ variables $a_1$ and $v$ but only $1$ equation: $S_{25}=1275 \Rightarrow 25(a_1+12v)=1275$.