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CAT 2024 Slot 1 QA Question 20

Multiple choice (+3 / −1) · Algebra · Progression & Series · Try it, then check the answer and solution below.

CAT 2024 Slot 1QAAlgebra • Progression & SeriesModerate
Suppose x1,x2,x3,…,x100x_{1}, x_{2}, x_{3}, \ldots, x_{100} are in arithmetic progression such that x5=−4x_{5}=-4and $2 x_{6}+2 x_{9}=x_{11}+x_{13} , Then, x100x_{100} equals
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Answer and solution

Answer: B) -194

📌 Core Concept
In an arithmetic progression (AP), each term is given by xn=a+(n−1)d,wherex_n = a + (n-1)d , whereaisthefirsttermandis the first term andd$ is the common difference.
🔢 Step-by-Step Solution
1
Given:
x5=−4x_5 = -4
2x6+2x9=x11+x132x_6 + 2x_9 = x_{11} + x_{13}
2
Express terms using AP formula:
x5=a+4d=−4x_5 = a + 4d = -4                                                                                                                                                                                                                                                                                                                                                  �

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