Questions: Given the geometric sequence below, what are the missing terms? -20,,-1.25

Solution Steps

To find the missing terms in a geometric sequence, we need to determine the common ratio. We can do this by dividing the second known term by the first known term. Once we have the common ratio, we can use it to find the missing terms by multiplying the previous term by the common ratio.

The given geometric sequence is \( -20, \, ?, \, -1.25 \). We need to find the missing second term.

To find the common ratio \( r \), we use the relationship between the first and third terms: \[ r = \left( \frac{-1.25}{-20} \right)^{\frac{1}{2}} = 0.25 \]

Now that we have the common ratio, we can find the second term \( a_2 \) using the first term \( a_1 \): \[ a_2 = a_1 \cdot r = -20 \cdot 0.25 = -5.0 \]

Final Answer