What is the 9th term -1/18 1/6 -1/2
(-1/18)*(r)=(1/6)
find r.
geometric progression:
ar^(n-1)
a=1st term
r=ratio
n=nth term
http://www.mathsrevision.net/alevel/pages.php?page=33
To find the 9th term of the given sequence, -1/18, 1/6, -1/2, we first need to determine the pattern. Looking at the sequence, we can observe that each term alternates between negative and positive. Additionally, the denominators of the fractions seem to increase by a factor of 3 with each term.
Let's break down the pattern to understand it more clearly:
- The first term, -1/18, has the denominator 18.
- The second term, 1/6, has the denominator 6, which is three times larger than 18.
- The third term, -1/2, has the denominator 2, which is again three times larger than 6.
From this, we can conclude that the denominator of each term is obtained by multiplying the previous denominator by 3. Therefore, the 4th term will have a denominator of 2*3 = 6, the 5th term will have a denominator of 6*3 = 18, and so on.
Now that we understand the pattern, let's find the 9th term.
Starting with the second term, 1/6, we can multiply the denominator by 3 eight times to reach the denominator of the 9th term.
6 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 6 * 3^8 = 6 * 6561 = 39,366
So, the denominator of the 9th term will be 39,366.
Since the terms alternate between negative and positive, we know that the 9th term will be negative.
Therefore, the 9th term of the sequence -1/18, 1/6, -1/2 is -1/39366.