CAT 2020 Question Paper | Quants Slot 3

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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

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Explanatory Answer

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"

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