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

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Answer 1 · 2016-08-12T18:56:50

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

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

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