Thread: Find the function from a sequence.

1. Find the function from a sequence.

There are two sequences I am unable to solve and any help on this matter would be appreciated.

1,3,15,105,945,10395
2,4,16,256,65536,4294967296

2. I think the second sequence can be defined as

when n = 1, the answer is 2
when n > 1, f(n-1)^2

I am still having problems with the first sequence

3. 1)

1
1*3 = 3
3*5 = 15
15*7 =105
105*9 =945
945*11=10395
Hence the
$T_{n+1} = T_{n} \times {2n-1}

$

2)
2
2^2=4
4^2=16
16^2=256
256^2=65536
65536^2=4294967296

Hence
$T_{n+1} = (T_{n} ) ^2$

4. Originally Posted by vexiked
There are two sequences I am unable to solve and any help on this matter would be appreciated.

1,3,15,105,945,10395
Note here that:

1*3 = 3
3*5 = 15
15*7 = 105
105*9 = 945
945*11 = 10395

So we can say that if $a_1=1$, then $a_{n+1}=(2n+1)a_n$

Does this make sense?

2,4,16,256,65536,4294967296
Note here that

$2^1=2$
$2^2=4$
$4^2=16$
$16^2=256$
$256^2=65536$
$65536^2=4294967296$

Thus, if $a_1=2$, then $a_{n+1}=(a_n)^2$

Does this make sense?

5. Thank you all for you help! much appreciated!