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?

APatel Jan 7, 2021

#1**+1 **

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

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

APatel Jan 7, 2021

#2**+2 **

Recursive rule for the arithmetic sequence

next term = previous term + 2

a_{n+1 }= a_{n} + 2 where a_{1} = 1

Explicit rule for above =

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

So

a_{n} = 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

a_{n+ 1} = an + 2 where a_{1} =2

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

a_{n} = 2 n

CPhill Jan 7, 2021