CAT 2021 Progression Question (Medium)

Question

Consider a sequence of real numbers such that for all If then is equal to

Accepted Answer

Given and This is a recursive sequence. Compute few terms We see that the differences are 0, 1, 2, 3, ... From onward, it s an arithmetic progression with first term and increasing by . So, Wait this contradicts the given answer. But we missed a shift Note So ... So That sum is Then Put Final Answer

CAT 2021

Quantitative

Progression

Medium

Consider a sequence of real numbers $x_{1}, x_{2}, x_{3}, \ldots$ such that $x_{n+1}=x_{n}+n-1$ for all $n \geq 1 .$ If $x_{1}=-1$ then $x_{100}$ is equal to

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