Algebra 1 arithmetric sequence

Question

What is the next fraction in this sequence? Simplify your answer.

2

3

 ,  

13

18

 ,  

7

9

 ,  

5

6

what is the missing sequence

Answer 1

Hello, Jatoria.

Okay, so your sequence is:

2/3, 13/18, 7/9, 5/6

Okay, so to find the pattern, let's find a common denominator for them.

They all have a common denominator of 18, so let's find the equivalent fractions:

2/3 x 6/6 = 12/18

13/18 = 13/18

7/9 x 2/2 = 14/18

5/6 x 3/3 = 15/18

So, it is clear that the pattern is + 1/18

So, the next fraction is 15/18 + 1/18 = 16/18, but since it can be reduced by dividing top and bottom by 2,

then 16/18 ÷ 2/2 = 8/9

Therefore, the next fraction is 8/9