[Math] Nth term of a sequence

sequences-and-series

First of, I know this is quite easy but I can't really work it out.

I need find the rule for these sequences

$a.$ $2, 3, 4.5, 6.25…$

$b$ $54, 18, 6, 2…$

$c$ $0.01, 0.1, 1, 10…$

My Steps

What I did first was find the differences between the numbers.

For question $a$ the difference between numbers goes $1$, $1.5$, $1.75$

For question $b$ the differnce between numbers goes $-36$, $-12$, $-4$. In this sequence I have found out that the number is being divided by $3$.

For question $c$ the difference between numbers goes $+0.09$, $+0.9$, $+9$. In this the term $9$ is being multiplied by $10$.

I am not sure what to do after. I can do the $nth$ term when it comes to numbers that go up the same and also squared, cubed and triangle numbers.

I know the general formula for $nth$ term is:

nth term = difference x n + (first term – difference).

I can't really use it though as the difference varies. Thanks!

Best Answer

Instead of differences, try the quotients between consecutive terms.