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

1 Answer

Answer:

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#