**24. Find three different formulas or rules for the terms of a sequence a_n if the first three terms of this sequence are 2, 3, 6.
**

**Solution: **We consider the first three terms of a sequence 2,3,6.

The simplest form of this sequence is

a_n=2^{n}-(n-1)

For n=1,2,3,...

We can even use recursive formula for this sequence, that is,

a_1=2

a_2=3

a_n=a_{n-1}.a_{n-2}

For n \geq 3

We can also formulate the nth term of this sequence by inserting factorials and doing inspection.

2=\frac{(1+1)!}{2^0}

3=\frac{(2+1)!}{2^1}

6=\frac{(3+1)!}{2^2}

Therefore, we have for n=1,2,3,...

a_n=\frac{(n+1)!}{2^{n-1}}

Hey there, You have done an incredible job. I’ll definitely digg it and personally recommend to my friends. I am confident they will be benefited from this web site.