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# Not a question, but need someone to clarify.

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So let's say we have an arithmetic sequence: 1, 3, 5, 7

How can I write this in recursive and explicit forms?

And let's say we have a geometric sequence 2, 4, 6, 8

How do I write this in explicit and recursive forms?

Jan 7, 2021

#1
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Oh I forgot, like I kinda know like for example, the explicit form of the arithmetic sequence is like an=1+2(n-1)

But my teacher showed things like with exponents, so I am completely lost there.

Jan 7, 2021
#2
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Recursive rule for the arithmetic  sequence

next term =  previous term +  2

an+1   = an + 2       where  a1  = 1

Explicit rule for  above  =

an = first term  +  d ( n -1)       where an  is the  nth term  and  d  =the common difference between terms = 2

So

an  = 1 +  2 ( n -1)

The second  ISN'T  a geometric series  because  the common ratio between  the terms is not constant

4/2  =2   but  6/4   =3/2

We can still write  rules for  it

Recursive rule

an+ 1  = an + 2  where a1  =2

Explicit rule =     an   = first term* (2)n     where n is the nth term ....so...

an =  2 n   Jan 7, 2021