Question

What are the next three terms in the series `{5/6,2/3,1/2,1/3,.........}`?

Answer 1

The next three numbers are `1/6, 0, -1/6`

Explanation:

Find the next 3 numbers in the arithmetic sequence `5/6, 2/3, 1/2, 1/3...`

The next number, or term, in an arithmetic sequence is formed by adding a number to the previous term. This number `d` is called the common difference.

To find the common difference, subtract the previous term from a term.

For example, if we subtract the 1st term from the 2nd, `2/3-5/6=-1/6` we get `d=-1/6`

Subtracting the 2nd term from the 3rd gives
`1/2-2/3=-1/6` and again `d=-1/6`

In fact, subtracting any term from the next term should give the same or "common" difference.

Now that we know `d=-1/6`, we can find the next term by adding it to the previous term.

In this example, we know the 4th term is `1/3`.

So, the 5th term is `1/3-1/6=1/6`

The 6th term is `1/6-1/6=0`

The 7th term is `0- 1/6=-1/6`