1
$\begingroup$

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)

$\endgroup$
  • $\begingroup$ Remember that not all studiy the same and in the same place: explain your symbols. $\endgroup$ – DonAntonio May 31 '16 at 15:29
  • $\begingroup$ @Joanpemo, i tried to explain the used symbols in my best English, i hope you understand. $\endgroup$ – Michelle_B May 31 '16 at 15:45
  • $\begingroup$ Thank you. Then, as noted in Schrodinger's answer, there is no one unique answer but infinite many. $\endgroup$ – DonAntonio May 31 '16 at 17:07
  • $\begingroup$ I think I indeed interpreted the question in my textbook wrong, I hope to give an update on this problem soon ^^ $\endgroup$ – Michelle_B May 31 '16 at 17:18
  • $\begingroup$ The number $v = a_{k + 1} - a_k$ for each positive integer $k$ is called the common difference. $\endgroup$ – N. F. Taussig Jun 1 '16 at 11:44
2
$\begingroup$

You have $2$ variables $a_1$ and $v$ but only $1$ equation: $S_{25}=1275 \Rightarrow 25(a_1+12v)=1275$.
Hence, infinite solutions are possible to your problem.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.