MEDAL!

Find the next three terms of the sequence.

Question

MEDAL!

Find the next three terms of the sequence.

calculusxy · Answer

$$\frac{1}{2}, \frac{1}{2}, \frac{3}{8}, \frac{1}{4}, \frac{5}{32},...$$

rebeccaxhawaii · Answer

is this all that is given?

calculusxy · Answer

yes

calculusxy · Answer

@Nnesha

calculusxy · Answer

@ganeshie8

ganeshie8 · Answer

Try $$\dfrac{n}{2^n}$$

calculusxy · Answer

how did you get that?

ganeshie8 · Answer

By eyeballing the pattern

calculusxy · Answer

omg it's working! how did you get it so quickly?

ganeshie8 · Answer

Plugin n=1,2,3,4,5 and convince yourself that it gives the first 5 terms of ur sequence correctly

ganeshie8 · Answer

Do a lot of problems and you will see the obvious patterns easily

calculusxy · Answer

thanks :) 

can you help me with a couple more?

ganeshie8 · Answer

Wil try

calculusxy · Answer

okay. so here they are:
4, 16, 36, 64, 100....

-9, 101, -999, 10001, -99999....

ganeshie8 · Answer

I don't want to give you the answer this time
There is a pretty obvious pattern in the first sequence

ganeshie8 · Answer

Look at the terms
Whats your first thought ?

dls · Answer

first sequence is so perfect XD

calculusxy · Answer

wait..

so it's like 2^2, 4^2, 6^2...

calculusxy · Answer

$$(2n)^2$$

is this good?

ganeshie8 · Answer

@DLS :)

ganeshie8 · Answer

You got it !
wat about the second sequence

ganeshie8 · Answer

Looks it is an interleaving of two sequences

calculusxy · Answer

yipee!

calculusxy · Answer

ok. i am trying this out

calculusxy · Answer

the second one looks a bit complicated to me. can you guide me through with this one?

dls · Answer

By the way..there is something called https://oeis.org/ . Many of you might be knowing about it, but for others, its pretty useful for analyzing some complex patterns. Just input first few terms of your series and it will tell you if there is some hidden secret pattern :)