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erogol
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Can i define a sequence which starts with a2. term or i must define the first term a1 as well
erogol said:Can i define a sequence which starts with a2. term or i must define the first term a1 as well
poutsos.A said: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
Focus said: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.
poutsos.A said: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
A sequence that can be started by the a2 term is a mathematical pattern in which each term is found by adding a constant number to the previous term. This constant number is called the common difference and is represented by the letter "d". The a2 term is the second term in the sequence, and it is used as the starting point for finding the rest of the terms.
When starting with the a2 term, the first term in the sequence can be found by subtracting the common difference (d) from the a2 term. This will give you the a1 term, which is the first term in the sequence.
Yes, a sequence can be started with any term. However, when starting with the a2 term, it is important to determine the common difference (d) in order to find the first term in the sequence. If the common difference is not known, it will be difficult to find the rest of the terms in the sequence.
The common difference (d) can be found by subtracting the a1 term from the a2 term. This will give you the constant number that is added to each term in the sequence to find the next term. Alternatively, if the first few terms in the sequence are given, the common difference can be found by subtracting any two consecutive terms.
Yes, a sequence started by the a2 term can have a negative common difference. This means that each term in the sequence will decrease by a constant number as you move further along the sequence. It is important to pay attention to the sign of the common difference in order to correctly find the terms in the sequence.