Geometric Progression — CAT Previous-Year Questions

Let the m-th and n-th terms of a geometric progression be 3/4 and 12, respectively, where m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

If a₁ + a₂ + a₃ + … + a_n = 3(2ⁿ⁺¹ – 2), for every n ≥ 1, then a₁₁ equals 

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

Which of the following best describes $a_n+b_n$ for even n?

If p = 1/3 and q = 2/3, then what is the smallest odd n such that a_n + b_n < 0.01?

On January 1, 2004 two new societies, S₁, and S₂, are formed, each with n members. On the first day of each subsequent month, S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r?

In a certain examination paper, there are n questions. For j = 1, 2, ..., n, there are 2^{(n − j)} students who answered j or more questions wrongly. If the total number of wrong answers is 4095, then the value of n is

If a₁ = 1 and a_n+1 = 2a_n + 5, n = 1, 2 ... , then a₁₀₀ is equal to

Let U_n+1 = 2U_n + 1 (n = 0, 1, 2, ...) and u₀ = 0. Then u₁₀ is nearest to