To find the missing term in the geometric sequence, we need to understand the properties of such sequences. In a geometric sequence, each term is found by multiplying the previous term by a constant, called the common ratio.
Given the terms 1250 and 50, we can find the common ratio. If we denote the missing term as ‘x’, then we have:
1250, x, 50
To find ‘x’, we can use the property of the common ratio:
Common Ratio (r) = 50 / x = x / 1250
This leads us to the equation:
50 / x = x / 1250
Cross-multiplying gives:
50 * 1250 = x * x
Therefore:
62500 = x²
Now, to find ‘x’, we take the square root of 62500:
x = √62500 = 250
Thus, a possible value for the missing term of the geometric sequence is 250.