Question

What is the next fraction in the sequence? Simplify your answer. 3/4, 5/8, 1/2, 3/8,

Answer 1

Answer: 2/8.

Step-by-step explanation:

When we have this type of problem, the usual way to solve them is trying with known types of sequences.

I will start with the arithmetic sequence, where the difference between any two consecutive terms is a constant. And if we call this difference as D, we will have the recursive relation:

Aₙ = Aₙ₋₁ + D

To check if this sequence is an arithmetic sequence, we can take the first two terms and see the difference:

(5/8 - 3/4) = (5/8 - 6/8) = -1/8.

Now let's do the same, but with the second and third terms:

(1/2 - 5/8) = (4/8 - 5/8) = -1/8

The difference is the same, -1/8.

Now we can use the recursive relationship above and the last given term of the sequence to find the next one:

A₅ = A₄ + (-1/8)

A₅ = 3/8 - 1/8 = 2/8

Then the next fraction in the sequence was 2/8.