Question

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what is the next term of the geometric sequence?
2, -10, 50,
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Explanation:

Step1: Find the common ratio \( r \)

In a geometric sequence, the common ratio \( r \) is found by dividing a term by its previous term. So, \( r=\frac{-10}{2}=-5 \).

Step2: Calculate the next term

To find the next term (the 4th term), we multiply the 3rd term (50) by the common ratio \( r \). So, the next term is \( 50\times(-5)= -250 \).

Answer:

\(-250\)