what is the 10th term in the geometric sequence? 400, 200, 100...?

Answer 1

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.

Answer 2

AAAaannndd the bot gets it wrong yet again!

a10 = 400 * (1/2)^9 = 400/512 = 25/32 = 0.78125

Answer 3

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.