Question

What is the next fraction in this sequence? Simplify your answer. 2/3, 1/3, 1/6, 1/12

Answer 1

`1/24`

Explanation:

In this sequence, it seems that you divide the number by `2` to get the next one in the sequence. Therefore, you would divide the last given number in the sequence, `1/12`, by `2`. Then it's just simple math.

`(1/12) / (2) = (1/12) xx (1/2) = 1/24`

Answer 2

`a_5=1/24`

Explanation:

`"these are the terms of a "color(blue)"geometric sequence"`

`a,ar,ar^2,ar^3, ...... ,ar^(n-1)`

`"where a is the initial term and r is the common ratio"`

`•color(white)(x)ar^(n-1)larrcolor(blue)"is the nth term"`

`•color(white)(x)r=a_2/a_1=a_3/a_2=...... =a^n/a^(n-1)`

`"here "r=(1/3)/(2/3)=(1/6)/(1/3)=(1/12)/(1/6)=1/2`

`rArra_5=2/3xx(1/2)^4=2/3xx1/16=2/48=1/24`