Question

How do you write the rule for the nth term given `1,10,100,1000,...`?

Answer 1

`t_n=10^(n-1), n in NN`

Explanation:

Let `t_n` denote the `n^(th)` term of the given seq., `n in NN`.

We have , `t_2/t_1=10, t_3/t_2=100/10=10, t_4/t_3=1000/100=10`..

This means that the seq. is a Geometric seq., with `t_1=1,` and, common ratio `r=10`

Hence, `t_n=t_1*r^(n-1)=1*(10)^(n-1)=10^(n-1), n in NN`