Function + Sequence and series questions please HELP!! (1 Viewer)

[a1079atw]

Hi all,

Could someone please help me with answering these three questions with working out?

(1) This one is from the hsc past papers - 1994 2U math


(2)
For this one, do I simply just sub n=1 and n=2 to find a1 and r? So for (d) do I do this:
p1= 2^-2=1/4 ;
p2=2^-1=1/2;
so r=(1/2)/(1/4)=2
and p1=(1/4)
Or is there other ways to solve it?

(2) And for this one... I totally have no idea how to solve it.



Please help me!
Thanks a lot

 

[Drongoski]

For Q2 - one way is to express the general term T_n in the form:



and simply read off the 1st term and the common ratio.




So here: a = 1/4 and r = 2



So a = 3 and r = 1/2

 

[a1079atw]

For Q2 - one way is to express the general term T[sb]n[/sub] in the form:



and simply read off the 1st term and the common ratio.




So here: a = 1/4 and r = 2



So a = 3 and r = 1/2

Thanks for the help!
but then for (b), wouldn't it be:

Then what will be? 6?

 

[TheMathStudent]

yup, you just have to sub in n=1 regardless of the rearrangement to get the first term a

 

[Drongoski]

Thanks for the help!
but then for (b), wouldn't it be:

Then what will be? 6?

Indeed and r=3. Isn't it neat - just using the template.

 

[a1079atw]

I see, thanks people!

 

[Drongoski]

people?

 

[a1079atw]

you and TheMathStudent