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

The last term can be expressed as a + (n-1)d. Here, 48 = 12 + 9d. Solving gives d = 4.

Using the sum formula, S_6 = 6/2 * (2*3 + 5*5) = 3 * 33 = 99.

Using the sum formula S_n = n/2 * (2a + (n-1)d), we have 60 = 6/2 * (8 + 5d). Solving gives d = 3.

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 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.

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

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 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.

Substituting x = 3 into the function gives f(3) = 2(3) + 1 = 6 + 1 = 7.

The transformation g(x) = 2(x - 1) + 3 indicates a horizontal shift to the right by 1 unit.

If the graph intersects the x-axis at x = 1 and x = 3, it means that f(1) = 0 and f(3) = 0, indicating the roots of the function.

The intersection of the graph with the x-axis indicates that the function value at that point is zero.

A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.

A parabola that opens upwards indicates that the function has a minimum value at its vertex.

A function is even if it is symmetric about the y-axis, meaning f(x) = f(-x) for all x.

A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).

A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).

Setting x = 0 in the equation gives y = 3, so the y-intercept is 3.

To find the x-intercept, set y = 0: 3x = 12, thus x = 4, giving the point (4, 0).

To find the y-intercept, set x = 0: 3(0) - 4y = 12, which gives y = -3.

To find the y-intercept, set x = 0 in the equation, resulting in y = -4. Thus, the y-intercept is 5.

To find the x-intercept, set y = 0. Solving gives x = 2, so the intersection point is (2, 0).

Setting y to 0 in the equation gives x = 2, so the intersection with the x-axis is (2, 0).