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?
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.
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
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
an+ 1 = an + 2 where a1 =2
Explicit rule = an = first term* (2)n where n is the nth term ....so...
an = 2 n