# CAT 2017 Question Paper | Quants Slot 2

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

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Question 34 : If a1 = $$frac{1}{2 × 5}$ , a2 = $\frac{1}{5 × 8}$ , a3 = $\frac{1}{8 × 11}$,...., then a1 + a2 + a3 + ...... + a100 is 1. $\frac{25}{151}$ 2. $\frac{1}{2}$ 3. $\frac{1}{4}$ 4. $\frac{111}{55}$ ## 2IIM : Best Online CAT Coaching #### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /-CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Progressions Given that a1 = $\frac{1}{2 × 5}$ , a2 = $\frac{1}{5 × 8}$ , a3 = $\frac{1}{8 × 11}$,...., We have to find a1 + a2 + a3 + ...... + a100 This can be done by partial fractions an = $\frac{1}{$3𝑛 − 1$(3𝑛 + 2)})
a1 = 3 - 1 = 2 , a2 = 6 - 1 = 5 , a3 = 9 – 1 = 8.
100th term = $$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 ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### 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? Phone:$91) 44 4505 8484
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