Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A sequence can be start by the a2 . term?

  1. Apr 4, 2009 #1
    Can i define a sequence which starts with a2. term or i must define the first term a1 as well
  2. jcsd
  3. Apr 4, 2009 #2


    User Avatar
    Science Advisor

    You can call the first term anything you want. It is merely a label.
  4. Apr 6, 2009 #3
    A sequence of real Nos is a function ,from the natural Nos N to the real Nos R.

    But a function from N TO R IS according to the definition of a function a subset of NxR ,such that for all nεN ,there exists a unique xεR ,SUCH that (n,x) BELONGS to the function.

    So if you ignore the 1st member ,strictly speaking you go against the definition of the sequence
  5. Apr 6, 2009 #4
    Not really, [itex]\{a_n\}_{n=1}^\infty \backslash \{a_1\}[/itex] is still a sequence, just take the map [itex]n \mapsto a_{n+1}[/itex]. It is perfectly well defined.
  6. Apr 13, 2009 #5
    What you have written is a subsequence of the sequence {[tex]a_{n}[/tex]}.So if you start the sequence { [tex]a_{n}[/tex]} from the No 2 ,lets say , the subsequence will start from ,2 as well ,hence violating the definition of the sequence
  7. Apr 13, 2009 #6
    Did you even read my post? It fits your definition perfectly.
  8. Apr 13, 2009 #7
    Use the definition of the subsequence correctly
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook