How it a Transistor an active device? Because it it not producing energy. We just feed it with energy and it amplifies it and that too not on his own but using a bias battery. So how it is considered to be an active device? Please can anyone provide full explanation?


Question: Can we represent this sequence as a function of n?
Answer: If we divide the terms by 4 we have $1,3,6,12,60,180...$ now we can proced to see a pattern, let's see the representation in prime numbers, $6=2\times 3$, $12=2^2\times 3$, $60=2^2\times 3 \times 5$ and $180=2^2\times 3^2 \times 5$, ...
So, taking $1=2^0$ and $3=2^0\times 3^1$ we have the list:
$2^0$
$2^0\times 3^1$
$2^1\times 3^1$
$2^2\times 3^1\times 5^0$
$2^2\times 3^1\times 5^1$
$2^2\times 3^2\times 5^1\times 7^0$


We see that the sum of the exponents of each line is $0,1,2,3,...$
When the sum of the exponents of each line is odd we add a new prime factor elevated to $0$.
Then the next two number in the sequence is:
$2^2\times 3^2\times 5^1\times 7^1=1260$
$2^2\times 3^2\times 5^2\times 7^1\times 11^0=6300$