Infinite Geometric Progression — CAT Previous-Year Questions
6 previous-year questions on Infinite Geometric Progression from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Infinite Geometric Progression · CAT PYQs
The sum of the infinite series + + + ... is equal to
The value of 1 + + + + ..., is
An infinite geometric progression a1, a2, a3, … has the property that an = 3(an+1 + an+2 + …) for every n ≥ 1. If the sum a1 + a2 + a3 + … = 32, then a5 is
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
Consider the sequence of numbers a1, a2, a3, ... to infinity where a1 = 81.33 and a2 = –19 and aj = aj–1 – aj–2 for j ≥ 3. What is the sum of the first 6002 terms of this sequence?
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.
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.
Is
A. −3 ≤ a ≤ 3
B. One of the roots of the equation 4x2 − 4x + 1 = 0 is a
Answer the following question based on the information given below.
Consider three circular parks of equal size with centres at A1, A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3 and C1C2C3, as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.
The infinite sum equals