what is the 10th term in the geometric sequence? 400, 200, 100...?
AAAaannndd the bot gets it wrong yet again!
a10 = 400 * (1/2)^9 = 400/512 = 25/32 = 0.78125
You are correct, I apologize for providing the wrong answer. The 10th term in the geometric sequence 400, 200, 100 is indeed 0.78125. Thank you for catching my mistake.
To find the 10th term in a geometric sequence, we need to determine the common ratio first.
The common ratio (r) in a geometric sequence is found by dividing any term by its preceding term. In this case, let's divide the second term by the first term:
200 / 400 = 0.5
Therefore, the common ratio for this sequence is 0.5.
Now that we know the common ratio, we can use the formula to find the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
Here, a_n represents the nth term, a_1 is the first term in the sequence, r is the common ratio, and (n-1) represents the position of the term we want to find.
So, to find the 10th term, we substitute the values into the formula:
a_10 = 400 * (0.5)^(10-1)
Simplifying:
a_10 = 400 * (0.5)^9
= 400 * 0.5^9
≈ 400 * 0.001953125
≈ 400 * 0.001953
≈ 0.78125
Therefore, the 10th term of the geometric sequence 400, 200, 100, ... is approximately 0.78125.
To find the 10th term in the geometric sequence 400, 200, 100, we need to first figure out the common ratio between each term.
We can do this by dividing any term by the preceding term. For example:
200/400 = 0.5
100/200 = 0.5
So the common ratio is 0.5.
To find the 10th term, we can use the formula:
an = a1 * r^(n-1)
where:
an = the nth term we want to find
a1 = the first term in the sequence
r = the common ratio
n = the position of the term we want to find
Plugging in our values:
a10 = 400 * 0.5^(10-1)
Simplifying:
a10 = 400 * 0.5^9
a10 = 6.25
Therefore, the 10th term in the geometric sequence 400, 200, 100 is 6.25.