# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Progressions Questions | Question 33

Has online preparation for CAT left you feeling all jittery ? Do you find yourself choosing among crossroads of what to prepare and what to skip ?
Worry not! CAT previous year paper will give you the much required direction and practicing these questions will give you a subtle nudge that'll help you move forward in your online CAT Preparation. Don't wait! Start right away with this question on Progressions taken from CAT Question Paper 2017.

Question 33 : An infinite geometric progression a1, a2, a3,... has the property that an = 3(an+1 + an+2 +....) for every n โฅ 1. If the sum a1 + a2 + a3 +...... = 32, then a5 is

1. $$frac{1}{32}$ 2. $\frac{2}{32}$ 3. $\frac{3}{32}$ 4. $\frac{4}{32}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Progressions The sum up to infinity, a1 + a2 + a3 +...... = 32. It can also be written as $\frac{๐}{1 โ ๐}$ = 32. We have been given that, an = 3$an+1 + an+2 +....) if n โฅ 1.
When n = 1, we get,
a = 3(a2 + a3 + .....)
โน a = $$frac{3๐๐}{1 โ ๐}$ [Since, a2 + a3 +...... = $\frac{๐r}{1 โ ๐}$] โน 1 โ r = 3r โน 1 = 4r โน r = $\frac{1}{4}$ Now finding the value of a is easy. a = 32 ร$1 - $$frac{1}{4}$) โน a = 32 ร $\frac{3}{4}$ โน a = 24 The value of a5 = ar4 , where a = 24 and r4 =$$$frac{1}{4}$)4 a5 = 24 ร $\frac{1}{4}$ ร $\frac{1}{4}$ ร $\frac{1}{4}$ ร $\frac{1}{4}$ Hence a5 = $\frac{3}{32}$ The question is "An infinite geometric progression a1, a2, a3,... has the property that an = 3$an+1 + an+2 +....) for every n โฅ 1. If the sum a1 + a2 + a3 +...... = 32, then a5 is"

##### Hence, the answer is $$frac{3}{32}$ Choice C is the correct answer ย ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com