find the 9th term of the g.s 5, 5/2, 5/4....
Well, let's see. To find the 9th term of a geometric sequence, we'll need to use the formula:
\(a_n = a_1 * r^{(n-1)}\)
Here, \(a_1\) is the first term, and \(r\) is the common ratio. In this case, \(a_1 = 5\) and \(r = \frac{1}{2}\).
So, the 9th term (\(a_9\)) will be:
\(a_9 = 5 * \left(\frac{1}{2}\right)^8\)
Now, let's calculate it:
\(a_9 = 5 * \frac{1}{256} = \frac{5}{256}\)
So, the 9th term of the geometric sequence is \(\frac{5}{256}\).
And here's a little joke to celebrate our calculation: Why was the math book sad? Because it had too many problems!
To find the 9th term of the geometric sequence 5, 5/2, 5/4..., we can first determine the common ratio of the sequence by dividing any term by its previous term.
The common ratio (r) is calculated as follows:
r = (5/2) / 5 = 1/2
Now that we know the common ratio, we can use the formula to find the nth term of a geometric sequence:
tn = a * r^(n-1)
In this case, the first term (a) is 5, and we want to find the 9th term (n = 9).
Using the formula:
t9 = 5 * (1/2)^(9-1)
Simplifying the equation:
t9 = 5 * (1/2)^8
t9 = 5 * 1/256
t9 = 5/256
Therefore, the 9th term of the geometric sequence 5, 5/2, 5/4... is 5/256.
To find the 9th term of a geometric sequence (g.s) with a common ratio, you can use the formula:
nth term = a * r^(n-1),
where "a" is the first term of the sequence, "r" is the common ratio, and "n" is the term number.
In the given geometric sequence, the first term (a) is 5 and the common ratio (r) is 1/2.
Plugging these values into the formula, we can calculate the 9th term:
9th term = 5 * (1/2)^(9-1)
= 5 * (1/2)^8
= 5 * 1/256
= 5/256
Therefore, the 9th term of the geometric sequence 5, 5/2, 5/4... is 5/256.