# How do you write the rule for the nth term given 1/20,2/30,3/40,4/50,...?

Aug 12, 2016

${T}_{n} = \frac{n}{10 \left(n + 1\right)} \mathmr{and} \frac{n}{10 n + 10}$

#### Explanation:

When trying to find the rule for the $n t h$ term, it is useful to write the numbers for $n , \text{ie} 1 , 2 , 3 , 4 , \ldots$ above or below the terms of the sequence.

Then compare the numbers in the term with $n$ and look for a pattern.

In this sequence:

1/20,2/30,3/40,4/50,... (larr"numerator the same as " n)/(larr"denominator same as 10 x (n+1)"

$1 , \text{ " 2," " 3," } 4$

So write that in terms of $n$

${T}_{n} = \frac{n}{10 \left(n + 1\right)} \mathmr{and} \frac{n}{10 n + 10}$