What is the 10th term of the geometric sequence 400, 200, 100?

The geometric sequence given is 400, 200, 100. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant factor, known as the common ratio.

To find the common ratio (r), we can divide the second term by the first term:

r = second term / first term = 200 / 400 = 0.5

We can also verify this ratio by dividing the third term by the second term:

r = third term / second term = 100 / 200 = 0.5

Now, we have established that the common ratio is 0.5.

The formula for the nth term (T_n) of a geometric sequence can be expressed as:

Tn = a * r(n-1)

where a is the first term, r is the common ratio, and n is the term number.

For our sequence:

• a = 400
• r = 0.5
• n = 10

Plugging these values into the formula to find the 10th term:

T10 = 400 * (0.5)(10-1) = 400 * (0.5)9

Now, we calculate:

(0.5)9 = 0.001953125

Then, we multiply:

T10 = 400 * 0.001953125 = 0.78125

Therefore, the 10th term of the geometric sequence is 0.78125.