The speed of a common snail is about 1 mm per second. It secretes a bit of mucus that coats the ground beneath and helps it to move along. This snail we are interested in now has a problem with this secretion and so it moves one mm in the first second and in the subsequent seconds it moves only half the distance covered in the previous second. Algae, the good it cherishes, is at 3 mm distance from this snail. In how much time it will reach its food? OptionsIt will never reach its food 2.5 seconds 2.7685 seconds 3 seconds

The snail moves 1 mm in the first second. In the second second, it moves half the distance of the previous second, which is 0.5 mm. So, by the end of the second second, it has moved a total of 1.5 mm. In the third second, it moves half the distance of the previous second, which is 0.25 mm. So, by the end of the third second, it has moved a total of 1.75 mm.

The snail continues to move in this manner, moving half the distance of the previous second each subsequent second. This is a geometric series with the first term a = 1 (the distance moved in the first second) and the common ratio r = 0.5 (each term is half the previous term).

The sum S of the first n terms of a geometric series is given by the formula S = a * (1 - r^n) / (1 - r). We want to find the smallest n such that S >= 3 (the snail has reached its food).

Substituting the given values into the formula, we get S = 1 * (1 - 0.5^n) / (1 - 0.5). Solving this inequality for n gives n > log(1 - 2*(3-1)) / log(0.5) = 2.58496...

Therefore, the snail will reach its food in just over 2.5 seconds. So, the correct answer is "2.7685 seconds".