Question

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

Answer 1

`T_n = n/(10(n+1))or n/(10n +10)`

Explanation:

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:

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

`1," " 2," " 3," " 4`

So write that in terms of `n`

`T_n = n/(10(n+1))or n/(10n +10)`