A geometric sequence is a sequence of numbers in which the ratio of any two consecutive terms is constant. To find the missing term in the sequence with the known terms 50 and 450, we can denote the missing term as x.
To find the value of x, we can establish the following relationships based on the properties of a geometric sequence:
- The ratio between the first term (50) and the missing term (x) should equal the ratio between the missing term (x) and the second term (450).
Mathematically, we can express that as:
frac{x}{50} = frac{450}{x}
Cross-multiplying gives us:
x * x = 50 * 450
This simplifies to:
x² = 22500
To find x, we can take the square root of both sides:
x = √22500
Calculating this, we find:
x = 150
This means the possible missing term in the geometric sequence that includes 50 and 450 is 150.
To summarize, in the geometric sequence containing the terms 50 and 450, the missing term is likely to be 150.