How can you represent the terms of a sequence explicitly? How can you represent them recursively?

Provide mathematical examples to support your opinions.

Question

How can you represent the terms of a sequence explicitly? How can you represent them recursively? 

Provide mathematical examples to support your opinions.

jamesj · Answer

For example 1, 2, 3, 4, 5, ...

An explicit way to write this would be $ a_n = n $. Now, what's a recursive definition for the same sequence?

perl · Answer

an+1= an + 1

jamesj · Answer

Yes, $$ a_{n+1} = a_n + 1 $$

Now, you make up another example for yourself.

perl · Answer

a(n+1) = a(n) + 1 , a(1) = 1

perl · Answer

james, can you help me with work problem?

jamesj · Answer

actually yes, what perl wrote just now is right. It's very important to give the first case

perl · Answer

can you do integrals?

jamesj · Answer

yes, give me the link and I'll help if I can

perl · Answer

http://openstudy.com/study#/updates/5113f11ce4b09e16c5c73f73

anonymous · Answer

@JamesJ Question...   What is the 15th term in the sequence using the given formula?

cn = 3n – 1  

Is 44 the right answer?

anonymous · Answer

Just wondering if I understood this all correctly.

jamesj · Answer

clearly, yes

anonymous · Answer

Thanks!

anonymous · Answer

Sorry, last question.. Is my recursive formula for 2,4,6,8,10,12,14,16,18,20. . . correct?
a(n)=a(n-1)+2

jamesj · Answer

Looks right to me!