# CAT 2020 Question Paper | Quants Slot 3

###### CAT Previous Year Paper | CAT Quants Questions | Question 1

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 x1 = -1 and xm = xm + 1 + (m + 1) for every positive integer m, then x100 equals

1. -5050
2. -5051
3. -5150
4. -5151

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

xm = xm + 1 + (m + 1)
Let's say k = m + 1
The equation now becomes: xk - 1 = xk + k
xk = xk - 1 - k
xk = - k + xk - 1

Now the vizualization of this equation becomes far simpler...
x1 = -1
x2 = -2 -1
x3 = -3 -2 -1
x4 = -4 -3 -2 -1

x100 = -100 -99 -98 ... -3 -2 -1
x100 = -(100 +99 +98 ... +3 +2 +1)
x100 = -($$frac{100$100+1$}{2})) = -5050

The question is "If x1 = -1 and xm = xm + 1 + (m + 1) for every positive integer m, then x100 equals"

##### Hence, the answer is, "-5050"

###### CAT Coaching in ChennaiCAT 2023

Classroom Batches Starting Now! @Gopalapuram

###### Best CAT Coaching in Chennai Introductory offer of 5000/-

Attend a Demo Class

##### 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 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com