CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

CAT Questions | Algebra | Progressions - Sum of infinite terms

The question is about Sum of a progression. A term is given and we need to find out the order of the term in 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 12: If Sn = n3 + n2 + n + 1 , where Sn denotes the sum of the first n terms of a series and tm = 291, then m is equal to?

1. 24
2. 30
3. 26
4. 10

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Method of solving this CAT Question from CAT Algebra - Progressions: How you would form the equation for this one?

Sn - Sn = tn
Sm - Sm-1 = tm
We know that Sn = n3 + n2 + n + 1

Hence m3 + m2 + m + 1
m3 + m2 + m + 1 - [(m-1)3 + (m-1)2 + (m-1) + 1 ] = 291
m3 + m2 + m + 1 - [m3 - 3m2 + 3m - 1 + m2 - 2m + 1 + m - 1 + 1] = 291
1 + 3m2 + 3m + 1 -2m - 1 = 291
-3m2 + m - 290 = 0
3m2 - m + 290 = 0

Solving above equation we get m = 10, $$frac{-29}{3}\\$ M cannot be negative as well as decimal as m is the term of the sequence. Hence m = 10 The question is "If Sn = n3 + n2 + n + 1 , where Sn denotes the sum of the first n terms of a series and tm = 291, then m is equal to?" Hence the answer is "10" Choice D is the correct answer. 🎉Special Independence day offer - get up to ₹ 10,000 off on our courses! ★ Register now 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
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