# CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

###### CAT Questions | Algebra | Progressions - Sequence and Series

The question is about sum of a series. A series is given and we need to find out the sum of the series. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 18: Find the sum of the series .4 + .44 + .444……. to n terms

1. 5.69
2. 14.44
3. $$frac{4}{81}\\$[9n-1+$\frac{1}{10^n}\\$] 4. $\frac{4}{81}\\$[n + 1] ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Progressions: Tough one to crack!! .4 + .44 + .444+……. to n terms = 4 * [0.1 +0.11 +0.111+……..to n terms] = $\frac{4}{9}\\$ * [0.9 +0.99 + 0.999+…….to n terms]$Multiplying and dividing by 9)
= $$frac{4}{9}\\$ * [$1-0.1)+(1-0.01)+(1-0.001)+…….to n terms]
= $$frac{4}{9}\\$ * [$1+1+1…..to n terms)-(0.1+0.01+0.001…to n terms)]
= $$frac{4}{9}\\$ * [ n - $\frac{\frac{1}{10} *$1 - $frac{1}{10^n}$}{1 - $frac{1}{10}}\\$ ] = $\frac{4}{9}\\$ * [n - $\frac{10^n - 1}{9 * 10^n}\\$ ] = $\frac{4}{9}\\$ * [n - $\frac{1}{9}\\$ *$1 - $$frac{1}{10^n}\\$)] = $\frac{4}{81}\\$ * [9n -$1 - $$frac{1}{10^n}\\$] = $\frac{4}{81}\\$ * [9n - 1 + $\frac{1}{10^n}\\$] The question is "Find the sum of the series .4 + .44 + .444……. to n terms" ##### Hence the answer is "$\frac{4}{81}\\$[9n-1+$\frac{1}{10^n}\\$]" Choice C is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### 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 Online Preparation | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Arithmetic Progressions Geometric Progressions Sample Questions ##### 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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com