CAT 2021 Progression Question (Hard)

Question

For a sequence of real numbers , if for all natural numbers , then the sum equals

Accepted Answer

Step 1 We are given that for all natural numbers , This is an alternating sum of terms in the sequence. Let denote the alternating sum up to . Step 2 We are asked to find Note Now subtract So Equation 1 Step 3 Now compute Now subtract So Now use Equation 1 So, Final Answer The value of is -2

CAT 2021

Quantitative

Progression

Hard

For a sequence of real numbers $x_1, x_2, \ldots, x_n$ , if $x_1 - x_2 + x_3 - \cdots + (-1)^{\,n+1} x_n = n^2 + 2n$ for all natural numbers $n$ , then the sum $x_{49} + x_{50}$ equals

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