# CAT 2021 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 16

CAT 2021 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 16 : Consider a sequence of real numbers $x_{1}, x_{2}, x_{3}, $ldots$ such that $x_{n+1}=x_{n}+n-1$ for all $n $geq 1 .$ If $x_{1}=-1$ then $x_{100}$ is equal to 1. 4949 2. 4849 3. 4850 4. 4950 ## 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 xn+1 = xn + n - 1 x1 = -1 x2 = x1 +$1 - 1$
x3 = x2 + (2 - 1)
x3 = x1 + (1 - 1) + (2 - 1)
x4 = x3 + (3 - 1)
x4 = x1 + (1 - 1) + (2 - 1) + (3 - 1)
Similarly we see that,
x100 = x1 + (1 - 1) + (2 - 1) + (3 - 1) + … + (99 - 1)
x100 = x1 + (1 + 2 + 3 + 4 + … + 98 + 99) - 99 (1)
x100 = x1 + (1 + 2 + 3 + 4 + … + 98)
x100 = (-1) + ($$frac { 98 $times 99 } { 2 }$$ x100 =$-1) + 4851
x100 = 4850

The question is " Consider a sequence of real numbers $x_{1}, x_{2}, x_{3}, $ldots$ such that $x_{n+1}=x_{n}+n-1$ for all $n $geq 1 .$ If $x_{1}=-1$ then $x_{100}$ is equal to " ##### Hence, the answer is '4850' Choice C 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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