Write the rule for the nth term given $\frac{1}{20},\frac{2}{30},\frac{3}{40},\frac{4}{50},...$

Nasir Sullivan
2022-09-23
Answered

Write the rule for the nth term given $\frac{1}{20},\frac{2}{30},\frac{3}{40},\frac{4}{50},...$

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Adelaide Barr

Answered 2022-09-24
Author has **9** answers

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:

$\frac{1}{20},\frac{2}{30},\frac{3}{40},\frac{4}{50},...\frac{\leftarrow \text{numerator the same as}\phantom{\rule{1ex}{0ex}}n}{\leftarrow \text{denominator same as 10 x (n+1)}}$

1, 2, 3, 4

So write that in terms of n

$T}_{n}=\frac{n}{10(n+1)}\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}\frac{n}{10n+10$

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

In this sequence:

$\frac{1}{20},\frac{2}{30},\frac{3}{40},\frac{4}{50},...\frac{\leftarrow \text{numerator the same as}\phantom{\rule{1ex}{0ex}}n}{\leftarrow \text{denominator same as 10 x (n+1)}}$

1, 2, 3, 4

So write that in terms of n

$T}_{n}=\frac{n}{10(n+1)}\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}\frac{n}{10n+10$

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