Angle Between A Line And A Plane

A harmonic progression (HP) is the sequence of numbers whose reciprocals form an arithmetic progression (AP). Let be a harmonic progression.
Then, the reciprocals form an arithmetic progression. Let the terms of this AP be denoted by , where: Given that and , we know the values of and . The general term of an arithmetic progression is given by: where is the common difference. Substituting the known values for and , we have:
Simplifying: Thus, the common difference is .
Now, the general term of the harmonic progression is: Substituting and , we get:
Simplifying the expression: Now, to find the least such that , we need to solve the inequality: Multiplying through by 475: Thus, the least integer is . Therefore, the correct answer is Option D.