Pre-cal... I'm dumb after the summer break... Questions within... ...?

Question

1st day today, we're doing easy stuff for now but I can't get some some of it. {1,4,7...} tn=3(n-1)+1 <----- I understand that

tn=(t(n-1))+3 <------ & I know how to get the recursive form

BUT...

How can I do this fir this type of sequence {2,4,8...}(multiplication ones)?

& exponential seems easy, but amidoinitrite? I'll make one up for myslef n try

{1,4,9...} non-recursive ---> tn=n^2 recursive -> tn=(sqrt(t(n-1)))^2

haha sorry if the last equation is hard to understand.

please help. the main thing I want is the one in the middle(multiplication one, but plz help w/ the last too. plz go into details with the middle one and show little examples.

Thanks in advance! I hope you can help me out!

Answer 1

The exponential recursive formula looks wrong.  It should be:

tn = (sqrt(t(n-1)) + 1)^2

For the middle one, just think of it in terms of words.  You&#039;re basically just multiplying the previous term by 2 so the recursive formula should be easy.

tn = 2*t(n-1)

The non-recursive one is kind of tricky.  Each successive term needs to be twice as high as the previous term so for bigger terms, you need to &quot;multiply by more 2&#039;s&quot;.  This can be accomplished by exponents.

tn = 2^n