The correct answer to this is 1.5. A geometric sequence is a set or sequence of numbers in which every term is mulptlied by a fixed, non-zero number or common ratio to get the succeeding term. The sequence described in the question is
\(a, 50, b, 112.5\)
where a is the first term and b is the third term. The first term a is multiplied by a common ratio R to get 50, then 50 is multiplied again by R to get the erd term b, and b is multiplied by thr common ratio R to get 112.5, or in mathematical terms:
R × 50 × R = 112.5
\(R^{2} = \frac{112.5}{50} \\ R^{2} = \frac{9}{4} \\ R = \sqrt{ \frac{9}{4} } \\ R = \frac{3}{2} = 1.5\)
