The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for Free) head out here: CAT Official Question Mocks. In CAT 2018 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank
Question 5 :Let t1, t2,.....be real numbers such that t1+ t2 +... + tn = 2n2 + 9n + 13, for every positive integer n ≥ 2. If tk=103, then k equals[TITA]
Let t1, t2,.....be real numbers such that t1+ t2 +... + tn = 2n2 + 9n + 13
If tk = 103 we have to find the value of k.
Let us assume this as sum to n terms i.e.
Sn = t1+ t2 +... + tn = 2n2 + 9n + 13
Given an expression in terms of n we can also take sum to n-1 terms i.e.
Sn-1 = t1+ t2 +... + tn-1 = 2(n-1)2 + 9(n-1) +13
This Sn and Sn-1 can be subtracted one from the another such that,
Sn = t1+ t2 +... + tn = 2n2 + 9n + 13
Sn-1 = t1+ t2 +... + tn-1 = 2(n-1)2 + 9(n-1) +13
Sn - Sn-1 = tn = 2n2 + 9n + 13 - 2(n-1)2 - 9(n-1) - 13
Sn - Sn-1 = tn = 2n2 + 9n + 13 - 2(n-1)2 - 9n + 9 - 13
Sn - Sn-1 = tn = 2[n2 - (n-1)2] + 9
Sn - Sn-1 = tn = 2[n2 - n2 + 2n - 1] + 9
tn = 2[2n - 1] + 9
tn = 4n - 2 + 9
tn = 4n + 7
So tk = 4k + 7 = 103
k = \\frac{103 - 7}{4})
k = 24
The 24th term is 103
The question is "Let t1, t2,.....be real numbers such that t1+ t2 +... + tn = 2n2 + 9n + 13, for every positive integer n ≥ 2. If tk=103, then k equals [TITA] "
Online Classroom Batches Starting Now!
Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.
Privacy Policy | Terms & Conditions
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093
Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com