Geometric Progression — CAT Previous-Year Questions
10 previous-year questions on Geometric Progression from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Geometric Progression · CAT PYQs
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 + … + an = 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
Answer the next 2 questions based on the information given below.
Let a1 = p and b1 = q, where p and q are positive quantities.
Define:
an = pbn−1 bn = qbn−1, for even n > 1 and
an = pan − 1 bn = qan − 1, for odd n > 1.
Which of the following best describes for even n?
Answer the next 2 questions based on the information given below.
Let a1 = p and b1 = q, where p and q are positive quantities.
Define:
an = pbn−1 bn = qbn−1, for even n > 1 and
an = pan − 1 bn = qan − 1, for odd n > 1.
If p = 1/3 and q = 2/3, then what is the smallest odd n such that an + bn < 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?
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
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 an+1 = 2an + 5, n = 1, 2 ... , then a100 is equal to
Use the following information:
Eighty five children went to an amusement park where they could ride on the merry – go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
Let Un+1 = 2Un + 1 (n = 0, 1, 2, ...) and u0 = 0. Then u10 is nearest to