# CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

###### CAT Questions | Algebra | Progressions - Arithmetic Progression CAT Questions

The question is about two arithmetic progressions. A question on possible smallest value again. We need to find out the smallest possible value of n which satisfies the given condition. 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 9: The sum of 2n terms of A.P. {1, 5, 9, 13…..} is greater than sum of n terms of A.P. = {56, 58, 60..…}. What is the smallest value n can take?

1. 9
2. 10
3. 12
4. 14

## 40 Hours of Sample classes. Signup to check now!

### Video Explanation

Arithmetic Progression

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2020Online Batches Available Now!

##### Method of solving this CAT Question from CAT Algebra - Progressions: Comparing two arithmetic progressions!

First A.P., a = 1, d = 4
S2n = $$frac{2n}{2}\\$ [2 * 1+$2n −1)4]
S2n = n(2 + 8n – 4) = n(8n – 2) = 8n2 – 2n
For the second AP, a = 56, d = 2
Sn = $$frac{n}{2}\\$ [2 * 56+$n −1)2]
Sn = $$frac{n}{2}\\$ [112+2n −2] = $\frac{2n}{2}\\$$110+2n)
Sum of 2n terms of AP {1, 5, 9, 13, …..} is greater than sum of n terms of A.P. = {56, 58, 60, …}
8n2 – 2n > $$frac{n}{2}\\$$110+2n)
16n2 – 4n > 110n + 2n2
14n2 > 114n
7n > 57
n > $$frac{57}{7}\\$ The smallest value n can take = 9. The question is "What is the smallest value n can take?" ##### Hence the answer is "9" Choice A is the correct answer. ###### Signup and Sample 9 full classes for Free ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 35,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiRegister Online, get Rs 7000/- off Attend a Demo Class ## 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