# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Progressions Questions | Question 34

CAT Previous Year Papers suggest that Progressionshave been an important part of the question asked in the CAT Examover the years, making it important for you to go through the CAT previous year paper to get a hang of the question types, pattern and their level of difficulty so that you can judge the complexity of these questions in your CAT Question Paper. 2IIM has analyzed previous year CAT papers for you and there are important takeaways from this analysis that'll help you better your CAT preparation online. Take a look at these insights by visiting 2IIM's CAT Blueprint.
To solve more questions like these, visit 2IIM's Question Bank!

Question 34 : If a1 = $$frac{1}{2 × 5}$ , a2 = $\frac{1}{5 × 8}$ , a3 = $\frac{1}{8 × 11}$,...., then a1 + a2 + a3 + ...... + a100 is 1. $\frac{25}{151}$ 2. $\frac{1}{2}$ 3. $\frac{1}{4}$ 4. $\frac{111}{55}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Progressions Given that a1 = $\frac{1}{2 × 5}$ , a2 = $\frac{1}{5 × 8}$ , a3 = $\frac{1}{8 × 11}$,...., We have to find a1 + a2 + a3 + ...... + a100 This can be done by partial fractions an = $\frac{1}{$3𝑛 − 1$(3𝑛 + 2)})
a1 = 3 - 1 = 2 , a2 = 6 - 1 = 5 , a3 = 9 – 1 = 8.
100th term = $$frac{1}{$(3 × 100$ − 1)((3 × 100) + 2)})
a1 = $$frac{1}{2}$ - $\frac{1}{5}$ = $\frac{5 - 2}{2 × 5}$ = $\frac{3}{2 × 5}$ a2 = $\frac{1}{5}$ - $\frac{1}{8}$ = $\frac{8 - 5}{5 × 8}$ = $\frac{3}{5 × 8}$ But these are not of the form $\frac{1}{$3𝑛 − 1$(3𝑛 + 2)}). Hence these are written as,
$$frac{1}{3}$[$\frac{1}{2}$ - $\frac{1}{5}$] = $\frac{5 - 2}{2 × 5}$ = $\frac{3}{2 × 5}$ × $\frac{1}{3}$ = $\frac{1}{2 × 5}$ $\frac{1}{3}$[$\frac{1}{5}$ - $\frac{1}{8}$] = $\frac{8 - 5}{5 × 8}$ = $\frac{3}{5 × 8}$ × $\frac{1}{3}$ = $\frac{1}{5 × 8}$ Hence this can be written as, $\frac{1}{3}$[$$$frac{1}{2}$ - $\frac{1}{5}$) +$$$frac{1}{5}$ - $\frac{1}{8}$) +$$$frac{1}{8}$ - $\frac{1}{11}$) + ....+$$$frac{1}{299}$ - $\frac{1}{302}$)] ⟹ $\frac{1}{3}$ [$\frac{1}{2}$ - $\frac{1}{302}$] ⟹ $\frac{1}{3}$ [$\frac{151 - 1}{302}$] ⟹ $\frac{1}{3}$ [$\frac{150}{302}$] ⟹ $\frac{50}{302}$ = $\frac{25}{151}$ The question is "If a1 = $\frac{1}{2 × 5}$ , a2 = $\frac{1}{5 × 8}$ , a3 = $\frac{1}{8 × 11}$,...., then a1 + a2 + a3 + ...... + a100 is" ##### Hence, the answer is $\frac{25}{151}$ Choice A 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 ###### 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