The reciprocals of the terms are 1/3 and 1/6. The common difference is (1/6 - 1/3) = -1/6. The third term's reciprocal will be 1/6 - 1/6 = 0, which means the third term is 1/12, thus the answer is 12.

The reciprocals of the first two terms are 1/3 and 1/6. The common difference is 1/6 - 1/3 = -1/6, which is incorrect. The correct common difference is 1/3 - 1/6 = 1/6.

The reciprocals of 3 and 6 are 1/3 and 1/6, which are in arithmetic progression.

The reciprocals of the terms are 1/4 and 1/2. The common difference is 1/2 - 1/4 = 1/4.

The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8. The third term's reciprocal will be 1/8 - 1/8 = 0, hence the third term is 16.

The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8, which means the common difference of the corresponding arithmetic progression is 1/8.

The first term is 5, and the second term in the harmonic progression corresponds to the reciprocal of the second term in the arithmetic progression, which is 5 + 2 = 7. Thus, the second term is 1/7.

The reciprocals are 1/5 and 1/10. The common difference is 1/10 - 1/5 = -1/10, which is the difference in the arithmetic progression.

The reciprocals are 1/5 and 1/10. The common difference is -1/10. The reciprocal of the third term is 1/10 - 1/10 = 1/15, so the third term is 15.

The nth term of a harmonic progression can be expressed as 1/(1/a + (n-1)d) where d is the common difference of the corresponding arithmetic progression.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here, m = 3 and b = -2, so the equation is y = 3x - 2.

The slope indicates the steepness of the line, representing the ratio of the rise over the run.

'b' is the coefficient of the linear term x in the quadratic equation.

The sum of the roots of a quadratic equation is given by -b/a. Here, -(-6)/1 = 6.

A negative coefficient for x^2 indicates that the parabola opens downwards.

A negative discriminant indicates that the roots are complex and conjugate.

The nth term of an AP is given by the formula a + (n-1)d. Here, a = 5, d = 3, and n = 10. Thus, the 10th term = 5 + (10-1) * 3 = 5 + 27 = 32.

If one equation is a multiple of another, they represent the same line, leading to infinitely many solutions.

Dependent equations represent the same line, leading to infinitely many solutions.

Inconsistent equations do not intersect, meaning there is no solution.

Let the common difference be d. From the equations 4 + 5d = 24, solving gives d = 4.

The 6th term is given by a + 5d. Here, it is x + 5*2 = x + 10.

Let the first term be a and the common difference be d. From the equations a + d = 10 and a + 3d = 14, we can solve for a and find it to be 8.

Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 3d = 14, solving gives a = 6.

Let the first term be a and the common difference be d. From the equations a + 2d = 12 and a + 6d = 24, we can find d = 3.

Let the first term be a and the common difference be d. From the equations a + 2d = 15 and a + 5d = 24, we can solve for d, which gives d = 3.

Let the first term be a and the common difference be d. From the equations a + 3d = 20 and a + 6d = 26, we can solve for a and find it to be 12.

Let the first term be a and the common difference be d. From the given terms, we have a + 4d = 20 and a + 9d = 35. Solving these gives a = 10.

The sum of the first n terms is given by S_n = n/2 * (2a + (n-1)d). Here, S_8 = 8/2 * (20 + 35) = 4 * 55 = 220.

Using the formula for the last term, 48 = 12 + (10-1)d. Solving gives d = 4.