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avatar+421 

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
avatar+421 
+1

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
avatar+114361 
+2

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

 

 

cool cool cool

 Jan 7, 2021

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