The last term of an AP is given by a + (n-1)d. Here, 100 = 10 + (20-1)d. Solving gives d = 5.

The common difference d can be calculated using the formula for the nth term: a + (n-1)d = last term. Here, 12 + 9d = 48, solving gives d = 4.

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_10 = 10/2 * (2*7 + 9*2) = 5 * (14 + 18) = 5 * 32 = 160.

The nth term is given by a + (n-1)d. Here, a = 2, d = 3, and n = 15. So, the 15th term = 2 + (15-1) * 3 = 2 + 42 = 44.

The first term a = 2 and the common difference d = 3. The 15th term = a + (15-1)d = 2 + 42 = 44.

The common difference d can be found using the formula for the nth term. The last term is given by a + (n-1)d. Here, 48 = 12 + (8-1)d, solving gives d = 4.

Using the formula for the last term: a + (n-1)d = last term, we have 8 + 5d = 32. Solving gives d = 4.

The passage warns that neglecting social inequalities can lead to social unrest and instability, highlighting the urgency of addressing these issues.

The vertex of a quadratic function is crucial as it represents the maximum or minimum point of the graph.

The passage suggests that many believe inequalities are a recent issue, which is a misconception.

The passage clarifies that inequality is multifaceted and not limited to economic factors.

The passage highlights resistance from those in power as a major barrier to achieving equality.

Promoting economic growth without regulation is least likely to address social inequalities, as it may lead to greater disparities.

Ignoring social inequalities can lead to worsening economic conditions, as highlighted in the passage.

The passage discusses systemic factors rather than individual choices as contributors to social inequalities.

The passage does not mention government negligence as a reason for the persistence of inequalities.

The passage does not support the idea of promoting unregulated economic growth as a method to address inequalities.

The passage does not advocate for free market policies as a solution to inequalities.

A quadratic function is represented by a parabola, which can open upwards or downwards depending on the coefficient of the squared term.

Geometric progression does not relate to harmonic progression, as harmonic progression is defined through the reciprocals of an arithmetic progression.

The terms 1/2, 1/3, 1/4, and 1/5 are in harmonic progression, but 1/6 does not fit as its reciprocal does not maintain the arithmetic progression.

Since 1000 can be expressed as 10^3, we have 10^x = 10^3, thus x = 3.

1000 can be expressed as 10^3, so x + 1 = 3, leading to x = 2.

Since 1000 can be expressed as 10^3, we have 10^(x+2) = 10^3, thus x + 2 = 3, leading to x = 1.

Since 32 can be expressed as 2^5, we have 2^(x+3) = 2^5, thus x + 3 = 5, leading to x = 2.

Since 1/16 can be expressed as 4^(-2), we have 4^(x-1) = 4^(-2), thus x - 1 = -2, leading to x = -1.

Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.

Since 49 can be expressed as 7^2, we have 7^(2x) = 7^2, thus 2x = 2, leading to x = 1.

Since 1/49 can be expressed as 7^(-2), we have 7^x = 7^(-2), thus x = -2.

Substituting the values gives 2(2) + 3(3) = 4 + 9 = 13.