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

Answer:

A geometric series a geometric sequence.

Step-by-step explanation:

Given sequence is :

$-\frac{1}{3},\frac{1}{6},-\frac{1}{12},\frac{1}{24},-\frac{1}{48}$

We will check the nature of given sequence:

Firstly find the common difference

$\frac{1}{6}-(-\frac{1}{3})=-\frac{1}{12}-\frac{1}{6}$

$\frac{1}{2}\neq -\frac{1}{4}$

So, its not a arithmetic sequence.

Now check for geometric sequence.

Find the common ratio

$\frac{\frac{1}{6} }{-\frac{1}{3} }=\frac{-\frac{1}{12} }{\frac{1}{6} }$

$-\frac{1}{2}=-\frac{1}{2}$

So, a geometric series a geometric sequence.

That's the final answer.

Answer 2

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