What number should be added to each of the three numbers, 3,11 and 27 so that the resulting numbers form a geomatric sequence ?

Options

A. 2
B. 3
C. 4
D. 5

Answer

D

Explanation

If x is the number , then to have a geometric sequence , `(11+x)/(3+x)=(27+x)/(11+x)`.
Cross-multiplying yields `121+22x+x^(2)=81+30x+x^(2)` , and subtracting `x^(2)` and solving gives the desired solution.
An alternative solution is to backsolve. Determine which answer choice yields a sequence of 3 integers with a common ratio .