CAT 2019 Question Paper | Quants Slot 2

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Question 5 : Let a₁ , a₂ be integers such that a₁ - a₂ + a₃ - a₄ + ........ +(-1)^n-1 a_n = n , for n ≥ 1. Then a₅₁ + a₅₂ + ........ + a₁₀₂₃ equals

1. -1
2. 1
3. 0
4. 10

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Video Explanation

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Explanatory Answer

Given that a₁ - a₂ + a₃ - a₄ + ........ +(-1) ^n-1 a_n = n
So, a₁ = 1
a₁ - a₂ = 2 => a₂ = 1-2 = -1
a₁ - a₂ + a₃ = 3 => a₃ = 1
So, the series proceeds as 1, -1, 1, -1, ...
Then a₅₁ + a₅₂ + ........ + a₁₀₂₃ = 1 + (-1) + .... + 1
a₅₁ + a₅₂ + ........ + a₁₀₂₃ = 1

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The question is "Let a₁ , a₂ be integers such that a₁ - a₂ + a₃ - a₄ + ........ +(-1)^n-1 a_n = n , for n ≥ 1. Then a₅₁ + a₅₂ + ........ + a₁₀₂₃ equals"

Hence, the answer is 1

Choice B is the correct answer.