# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 20

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 20 : The value of $1+$left$1+$frac{1}{3}$right$ $frac{1}{4}+\left$1+$frac{1}{3}+\frac{1}{9}\right$ $frac{1}{16}+\left$1+$frac{1}{3}+\frac{1}{9}+\frac{1}{27}\right$ $frac{1}{64}+\cdots$, is 1. $\frac{15}{13}$ 2. $\frac{16}{11}$ 3. $\frac{27}{12}$ 4. $\frac{15}{8}$ ## 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 $1 + \left$ 1 + $frac { 1 } { 3 } \right$ $frac { 1 } { 4 } + \left$ 1 + $frac { 1 } { 3 } + \frac { 1 } { 3 ^ { 2 } } \right$ $frac { 1 } { 4 ^ { 2 } } + \left$ 1 + $frac { 1 } { 3 } + \frac { 1 } { 3 ^ { 2 } } + \frac { 1 } { 3 ^ { 3 } } \right$ $frac { 1 } { 4 ^ { 3 } } + \ldots$ The nth term in the series is given by, $T _ { n } = \left$ $right.$ Sum of $n$ terms of a GP with $\left. a = 1 , r = \frac { 1 } { 3 } \right$ $left$ $frac { 1 } { 4 } \right$ ^ { n - 1 }$ $T _ { n } = $left$ $frac { 1 - \left$ $frac { 1 } { 3 } \right$ ^ { n } } { 1 - $frac { 1 } { 3 } } \right$ $frac { 1 } { 4 ^ { n - 1 } } = \frac { \left$ 3 ^ { n } - 1 $right$ $times 3 } { 3 ^ { n } \times 2 } \left$ $frac { 1 } { 4 ^ { n - 1 } } \right$$ $T _ { n } = $frac { 1 } { 2 } \left$ $frac { 3 ^ { n } - 1 } { 12 ^ { n - 1 } } \right$ = $frac { 1 } { 2 } \left$ $frac { 3 } { 4 ^ { n - 1 } } - \frac { 1 } { 12 ^ { n - 1 } } \right$ = $frac { 3 } { 2 } \left$ $frac { 1 } { 4 } \right$ ^ { n - 1 } - $frac { 1 } { 2 } \left$ $frac { 1 } { 12 } \right$ ^ { n - 1 }$ So, we have decomposed the infinite series into two infinite series by decomposing the nth term. $$therefore S _ { \infty } = \frac { 3 / 2 } { 1 - 1 / 4 } - \frac { 1 / 2 } { 1 - 1 / 12 } = \frac { 3 / 2 } { 3 / 4 } - \frac { 1 / 2 } { 11 / 12 } = 2 - \frac { 6 } { 11 } = \frac { 16 } { 11 }$ The question is " The value of $1+\left$1+$frac{1}{3}\right$ $frac{1}{4}+\left$1+$frac{1}{3}+\frac{1}{9}\right$ $frac{1}{16}+\left$1+$frac{1}{3}+\frac{1}{9}+\frac{1}{27}\right$ $frac{1}{64}+\cdots$, is " ##### Hence, the answer is '$\frac{16}{11}$' Choice B is the correct answer. ###### 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 and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### 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
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