This question is from **Sequence and series**. Algebra is the second most **important topic** in Quant. Make sure you master this topic during your **CAT preparation**. In this question, an algorithm is given, which keeps on generating the numbers. We need to find the value of a particular sequence. Will something routine work or, do we have to think out of the box? Let's have a crack at this question and then check out how Rajesh deciphers this question for you!

Question 1 : If x_{1} = -1 and x_{m} = x_{m + 1} + (m + 1) for every positive integer m, then x_{100} equals

- -5050
- -5051
- -5150
- -5151

Valid until 1st Dec

Online Batches Available Now!

x_{m} = x_{m + 1} + (m + 1)

Let's say k = m + 1

The equation now becomes: x_{k - 1} = x_{k} + k

x_{k} = x_{k - 1} - k

x_{k} = - k + x_{k - 1}

Now the vizualization of this equation becomes far simpler...

x_{1} = -1

x_{2} = -2 -1

x_{3} = -3 -2 -1

x_{4} = -4 -3 -2 -1

x_{100} = -100 -99 -98 ... -3 -2 -1

x_{100} = -(100 +99 +98 ... +3 +2 +1)

x_{100} = -(\\frac{100(100+1)}{2})) = -5050

The question is **"If x _{1} = -1 and x_{m} = x_{m + 1} + (m + 1) for every positive integer m, then x_{100} equals" **

CAT 2021

Enroll at

44,000/-

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 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com