If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct?

1. y² = x²z²

2. y² = x² + z²

3. y² = xz

4. xyz = 1

Consider the G.P. a, ar, ar², …….., l. The kth term from the end is :

1. $\dfrac{l}{r^{k-1}}$

2. $\dfrac{l}{k}$

3. $\dfrac{al}{r^k}$

4. $\dfrac{l}{ar^{k-1}}$

The product of n terms of a G.P. with first term a and common ratio r, r > 1 is :

1. $\dfrac{a^n(r^{n} - 1)}{r - 1}$

2. aⁿrⁿ

3. $a^{n} r^{\dfrac{n(n+1)}{2}}$

4. $a^{n} r^{\dfrac{n(n-1)}{2}}$

Case Study

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, then

Based on the above given information, answer the following questions:

1. The number of bacteria that would be present at the end of 4th hour is :
   (a) 240
   (b) 480
   (c) 960
   (d) 450

2. The number of bacteria that would be present at the end of 10th hour is :
   (a) 30720
   (b) 15360
   (c) 61440
   (d) 27540

3. The number of bacteria that would be present at the end of nth hour is :
   (a) 30 × 2^{(n - 1)}
   (b) 30 × 2^{(n + 1)}
   (c) 30 × 2ⁿ
   (d) none of these

4. What would be the sum of the first 5 terms of the G.P. that is formed by the number of bacteria after the completion of each hour?
   (a) 450
   (b) 930
   (c) 1890
   (d) none of these

5. What would be the sum of the first n terms of the G.P. that is formed by the number of bacteria after the completion of each hour?
   (a) 30 × 2⁽ⁿ⁾ - 1
   (b) 30 × (2^{(n - 1)} - 1)
   (c) 30 × (2^{(n + 1)} - 1)
   (d) 30 × 2ⁿ - 30