Find the formula for the nth term of the following geometric progression 8/27,4/9,2/3
To find the formula for the nth term of a geometric progression, we need to first find the common ratio (r) of the sequence. We can do this by dividing any term (except the first term) by its previous term. Therefore:
r = (4/9) / (8/27) = (4/9) * (27/8) = 3/2
Now that we have the common ratio (r = 3/2), we can find the formula for the nth term by using the general formula for a geometric progression:
an = a1 * r^(n-1)
where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
Since we are given the first term (a1 = 8/27), we can plug in all the values:
an = (8/27) * (3/2)^(n-1)
Therefore, the formula for the nth term of the given geometric progression is (8/27) * (3/2)^(n-1).