CAT 2020 Question Paper | Quants Slot 3

CAT Questions

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 x_m = x_{m + 1} + (m + 1) for every positive integer m, then x₁₀₀ equals

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Video Explanation

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Explanatory Answer

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...
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

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

Hence, the answer is, "-5050"

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