What does this notation mean $\{a_k\}_{k=i}^n$?

I saw it in sites talking about sequences but there was no explanation of what it meant.

E: I reviewed the other post, this is not a duplicate, and the chosen answer described what I asked.

  • $\begingroup$ possible duplicate of Notation for sequences $\endgroup$ – M.K. Jun 12 '15 at 15:28
  • $\begingroup$ The other question asks what notation to write for infinite sequences; this question concerns how to read a notation which (it happens) is for finite sequences (or subsequences). This does not seem a duplicate to me. $\endgroup$ – David K Jun 13 '15 at 1:28

${\{a_k\}}_{k=i}^n$ means the list of terms in the sequence $a_k$, ranging from $k=i$ to $k=n$; i.e.:


  • $\begingroup$ I see! That was really simple. Thanks! $\endgroup$ – YoTengoUnLCD Jun 12 '15 at 15:23
  • $\begingroup$ You are very welcome. $\endgroup$ – Ant Jun 12 '15 at 15:23
  • $\begingroup$ I would assume $\{a_k\}_{k=i}^n$ was the set $\{a_i, \dots a_n\}$, but $(a_k)_{k=i}^n$ was the list $(a_i, \dots, a_n)$. $\endgroup$ – Thomas Ahle Jun 1 '19 at 15:23

It means the following collection of objects: $$\{a_k\}_{k=i}^n=\left \{ a_i,a_{i+1},a_{i+2},\dots,a_n \right \}$$

  • For example, if $i=1$ and $n=5$, we would have: $$\{a_k\}_{k=1}^5=\left \{ a_1,a_{2},a_{3},a_{4},a_5 \right \}$$

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