Using the formula for the nth term, a + (n-1)d = 7 + (8-1)(-2) = 7 - 14 = -7.

Using the formula for the nth term, a + (n-1)d = 7 + 14*2 = 7 + 28 = 35.

The nth term is given by a + (n-1)d. Here, a = 7, d = -2, and n = 6. So, the 6th term = 7 + (6-1)(-2) = 7 - 10 = -3.

Using the formula for the last term, l = a + (n-1)d, we have 37 = 7 + (16-1)d. Solving gives d = 2.

Using the formula for the nth term, we have 50 = 8 + (10-1)d. Solving for d gives us d = 5.

The nth term of an arithmetic sequence is given by a + (n-1)d. Here, a = 5, d = 3, n = 10. So, 5 + (10-1)3 = 32.

In an arithmetic series, the last term can be expressed as a + (n-1)d. Here, 48 = 12 + (10-1)d. Thus, 48 - 12 = 9d, giving d = 4.

a_n = a + (n-1)d = 5 + (15-1) * 3 = 5 + 42 = 47.

The reciprocals are 1, 2, and 3, which are in arithmetic progression. The next term in the sequence of reciprocals is 4, so the fourth term is 1/4.

The reciprocals are 1, 2, and 3. The common difference is 2 - 1 = 1.

The reciprocals of the terms form an arithmetic progression: 2, 3, and x. The common difference is 1. Therefore, x = 6.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression, hence 1/a + 1/b = 1/c.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression, which leads to the relationship 1/a + 1/c = 2/b.

In a harmonic progression, the reciprocals of the terms are in arithmetic progression, hence 1/a, 1/b, 1/c are in AP.

The conclusion cannot be definitively drawn from the premises provided.

Concave lenses always produce virtual and erect images regardless of the object distance.

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 10 cm = 20 cm.

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.

Power P = 1/f (in meters). Thus, P = 1/0.25 = +4 D.

A negative focal length indicates that the lens is a concave lens.

Power (P) = 1/f (in meters). Here, f = 0.2 m, so P = 1/0.2 = +5 D.

Power (P) is given by P = 1/f (in meters). Thus, P = 1/0.25 m = +4 D.

Power is inversely proportional to focal length. If f is doubled, P = 1/f will halve.

The distance from the focus to the directrix is 4, so the equation is x^2 = 8y.

Range = Maximum - Minimum = 14 - 3 = 11

The numbers are already in order. The median is the average of the 5th and 6th numbers: (5 + 6) / 2 = 5.5.

According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium position to the left, favoring the reactants.

ΔTf = Kf * m; -5 = -1.86 * m; m = 5 / 1.86 = 2.68 m.

Freezing point depression = i * Kf * m = 2 * 1.86 °C kg/mol * 1 mol/kg = 3.72 °C. Thus, freezing point = 0 - 3.72 = -3.72 °C.

Freezing point depression = i * Kf * m = 2 * 1.86 * 1 = 3.72°C. Therefore, freezing point = 0 - 3.72 = -1.86°C.