Question

A student wrote the terms below. -1/3,1/6,-1/12,1/24,-1/48 What do these terms represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence

Answer 1

It is a geometric sequence because it is getting multiplied by 1/2. Hope this helps!

Answer 2

A geometric series a geometric sequence.

Explanation:

Given sequence is :

`-(1)/(3),(1)/(6),-(1)/(12),(1)/(24),-(1)/(48)`

We will check the nature of given sequence:

Firstly find the common difference

`(1)/(6)-(-(1)/(3))=-(1)/(12)-(1)/(6)`

`(1)/(2)\\eq -(1)/(4)`

So, its not a arithmetic sequence.

Now check for geometric sequence.

Find the common ratio

`((1)/(6) )/(-(1)/(3) )=(-(1)/(12) )/((1)/(6) )`

`-(1)/(2)=-(1)/(2)`

So, a geometric series a geometric sequence.

That's the final answer.