The nth term of a GP is given by a * r^(n-1). Here, a = 3, r = 2, and n = 5. Thus, the 5th term = 3 * 2^(5-1) = 3 * 16 = 48.

The 6th term is given by a * r^(n-1) = 4 * (1/2)^(6-1) = 4 * (1/32) = 4/32 = 0.125.

The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_4 = 5(1 - 0.5^4) / (1 - 0.5) = 5(1 - 0.0625) / 0.5 = 5 * 0.9375 / 0.5 = 9.375.

The last term can be expressed as a * r^(n-1). Here, 80 = 5 * r^(4-1) = 5 * r^3. Thus, r^3 = 16, giving r = 2.

Let the common ratio be r. The terms are 5, 5r, 5r^2, 5r^3. Setting 5r^3 = 80 gives r^3 = 16, thus r = 2.

The sum of the first n terms of a GP is given by S_n = a(1 - r^n)/(1 - r) for r ≠ 1.

The 3rd term of a GP is given by a * r^(n-1). Here, it is x * y^(3-1) = xy^2.

The sum of the first n terms of a geometric series is a(1 - r^n) / (1 - r). Here, a = 4, r = 2, n = 5. So, 4(1 - 2^5) / (1 - 2) = 4(1 - 32) / -1 = 124.

The nth term of a geometric series is given by ar^(n-1). Here, a = 4, r = 2, n = 6. So, 4 * 2^(6-1) = 4 * 32 = 128.

The nth term of a geometric series is given by a_n = ar^(n-1). Thus, a_4 = 4 * 3^(4-1) = 4 * 27 = 108.

Let the first term be a and the common ratio be r. Then, 3rd term = ar^2 = 27 and 5th term = ar^4 = 243. Dividing gives r^2 = 9, so r = 3. Substituting back gives a = 3.

The 6th term is given by 10 * (0.5)^(6-1) = 10 * (0.5)^5 = 10 * 0.03125 = 0.3125.

The 4th term is given by 2 * (-2)^(4-1) = 2 * (-8) = -16.

The 6th term is given by a * r^(n-1) = 4 * (1/2)^(6-1) = 4 * (1/32) = 0.125, which is 0.25.

The first four terms are 5, 2.5, 1.25, and 0.625. Their sum is 5 + 2.5 + 1.25 + 0.625 = 9.375.

Let the common ratio be r. The terms are 5, 5r, 5r^2, 5r^3. Setting 5r^3 = 80 gives r^3 = 16, thus r = 2.

The 6th term is given by 7 * (1/2)^(6-1) = 7 * (1/32) = 0.4375.

The nth term of a GP is given by a * r^(n-1). Thus, the 6th term = x * y^(6-1) = xy^5.

The gravitational potential energy is considered maximum at infinity, where it is defined to be zero.

To find the number of people who like either coffee or tea, use the formula: (Coffee + Tea - Both) = (60 + 40 - 20) = 80.

P(Football|Cricket) = P(Football and Cricket) / P(Cricket) = 10/60 = 1/6.

Using conditional probability, P(Football | Basketball) = P(Football and Basketball) / P(Basketball) = 10/30 = 1/3.

People who like only tea = Total tea lovers - Both tea and coffee lovers = 60 - 30 = 30.

People who like only football = Total football lovers - Both football and basketball lovers = 80 - 30 = 50.

The age 22 appears 3 times, which is more than any other age, so the mode is 22.

The number of people who like at least one sport is 90 + 60 - 30 = 120, so those who like neither is 150 - 120 = 30.

The number of people who like only cats is 60 - 30 = 30.

The number of people who like only non-fiction is: 60 - 30 = 30.

The number of people who like either tea or coffee is: 90 + 60 - 30 = 120. Therefore, those who like neither is: 150 - 120 = 30.

The number of people who like only action movies is 120 - 50 = 70.