# Write the rule for the nth term given 1/20,2/30,3/40,4/50,...

Write the rule for the nth term given $\frac{1}{20},\frac{2}{30},\frac{3}{40},\frac{4}{50},...$
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When trying to find the rule for the nth term, it is useful to write the numbers for n, ie 1,2,3,4,... 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:
$\frac{1}{20},\frac{2}{30},\frac{3}{40},\frac{4}{50},...\frac{←\text{numerator the same as}\phantom{\rule{1ex}{0ex}}n}{←\text{denominator same as 10 x (n+1)}}$
1, 2, 3, 4
So write that in terms of n
${T}_{n}=\frac{n}{10\left(n+1\right)}\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}\frac{n}{10n+10}$