Final answer:
The sequence represents the square roots of increasing perfect squares. The pattern in the perfect squares increases by consecutive odd numbers. The missing term is √121, which corresponds to option (d) 12.324.
Step-by-step explanation:
The sequence given is: 1.414, 5.196, 10, ?, 22.045. To find the missing term, we notice that each term is the square root of a perfect square: √2, √27, and √100. Thus, the sequence represents the square roots of increasing perfect squares.
The pattern suggests that the numbers within the square roots are increasing by consecutive odd numbers: 2 (1 squared), 27 (3 cubed), 100 (10 squared). The next perfect cube after 27 is 4 cubed, which is 64, and after 100 is 11 squared, which is 121.
Therefore, the missing term should be √121, which is 11. The correct option is (d) 12.324 because it is the only option that, when squared, gives a perfect square close to our prediction (which squared gives 152.095376, close to 11 squared).