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The given sequence is : $2\frac{1}{2}, 1\frac{7}{13}, 1\frac{1}{9}, \frac{20}{23}, ........$. I subtracted the 2nd and 1st term and the result was $-\frac{10}{13}$ and then the 3rd and 2nd term and the result was $-\frac{50}{117}$.

tomriddle99
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  • this could theoretically go on with any sets of values. For example, the next one could be $\pi/e$ and the one after $\sqrt{\pi}$. You gotta specify your sequence more precisely. – gt6989b May 24 '18 at 14:59
  • Any such sequence will have infinitely many "correct" ways to write a general term. Your calculation shows that it's not an arithmetic progression. If you edit the question to tell us where the terms you have come from perhaps we can help. – Ethan Bolker May 24 '18 at 14:59
  • But I found the question in this form only. It was from a set of questions our teacher gave us to do as homework. – tomriddle99 May 24 '18 at 15:00
  • 2nd and 4th terms are the same. is the idea that all even terms are the same and all odd ones form an arithmetic progression? – gt6989b May 24 '18 at 15:01
  • Perhaps there's something else useful where you "found the question". If not, then you are probably out of luck. – Ethan Bolker May 24 '18 at 15:01
  • sorry, I just edited the question as I saw that fourth term I wrote was different from the question. please see it now – tomriddle99 May 24 '18 at 15:05

1 Answers1

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It is simple now...

Your sequence is, $\frac{20}{8}, \frac{20}{13}, \frac{20}{18}, \frac{20}{23}, \cdots$

Observe that the denominator is in AP with the common difference of 5.

And clearly, the sequence is in harmonic progression.

Eval
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