A sequence can be start by the a2 . term?

1. Apr 4, 2009

erogol

Can i define a sequence which starts with a2. term or i must define the first term a1 as well

2. Apr 4, 2009

mathman

You can call the first term anything you want. It is merely a label.

3. Apr 6, 2009

poutsos.A

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

4. Apr 6, 2009

Focus

Not really, $\{a_n\}_{n=1}^\infty \backslash \{a_1\}$ is still a sequence, just take the map $n \mapsto a_{n+1}$. It is perfectly well defined.

5. Apr 13, 2009

poutsos.A

What you have written is a subsequence of the sequence {$$a_{n}$$}.So if you start the sequence { $$a_{n}$$} from the No 2 ,lets say , the subsequence will start from ,2 as well ,hence violating the definition of the sequence

6. Apr 13, 2009