Question

The second term in a geometric sequence is 50. the fourth term in the same sequence is 112.5. what is the common ratio in this sequence?

Answer 1

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) = (112.5)/(50) \\ R^(2) = (9)/(4) \\ R = \sqrt{ (9)/(4) } \\ R = (3)/(2) = 1.5`