HELP WILL GIVE MEDALS!! Write an explicit definition for the sequence -3,1,5,9,...

Question

anonymous · Answer

@Hero can you help

anonymous · Answer

@mathmale  can you help

myininaya · Answer

Hint: I wonder if this an arithmetic sequence.

mathmale · Answer

Hello, dmb97,

Take a good look at the first few terms of this sequence:  -3,1,5,9,... 

How do we obtain that 1 from -3?  that 5 from 1?

mathmale · Answer

There are two primary types of sequences that we learn at this level:  arithmetic and geometric.  Which do you think is the case in THIS particular sequence?

anonymous · Answer

a arithmetic and its +4

anonymous · Answer

x = 4*n + 1

mathmale · Answer

So you'd start with -3, add 4 and get 1.  Then you'd add 4 again and get 5.  And so on.  Looks like progress to me.

mathmale · Answer

Note that this is an ARITH. sequence.  When n=1, the first term of the seq. is -1.  When n=2 the second term of the sequence is 3.

Can you write an arithmetic sequence that produces these results?

mathmale · Answer

$$a _{n}=???$$

mathmale · Answer

$$a _{1}=-1$$

mathmale · Answer

$$a _{2}=a _{1}+?$$

mathmale · Answer

Your formula must involve n and must involve 4 in some manner.

mathmale · Answer

Sorry, but I need to get off the Internet soon.  Happy to help you, but need fast answers from you to stay engaged.

anonymous · Answer

a2=a1+4n

mathmale · Answer

or, more generally,$$a _{n+1{}}=a _{n}+4$$

mathmale · Answer

Check this out and determine whether or not it "works" for n = 1, 2, 3, 4, ... 

Unfortunately I have to get off the 'Net now.  Hope this discussion has been of some help to you.

mathmale · Answer

Please let me know how this problem ended for you.  Are you clear regarding what you were supposed to do, and with the formula we eventually obtained?  This is called a "recursive" formula, because each term of the sequence depends upon the previous term.  There's another way to write a formula for this arithmetic sequence.