# Difference between revisions of "User:Geometry285"

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Posting here until I find a place for an upcoming mock I’m creating | Posting here until I find a place for an upcoming mock I’m creating | ||

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[[G285 MC10A Problems/Problem 4|Solution]] | [[G285 MC10A Problems/Problem 4|Solution]] | ||

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+ | ==Problem 5== | ||

+ | Let a recursive sequence be denoted by <math>a_n</math> such that <math>a_0 = 1</math> and <math>a_1 = k</math>. Suppose <math>a_{n-1} = n+a_n</math> for <math>n>1</math>. Let an infinite arithmetic sequence <math>P</math> be such that <math>P=\{k, k+p, k+2p \cdots\}</math>. If <math>k</math> is prime, for what value of <math>p</math> will <math>k_{2021} = k-2022p+1</math>? | ||

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+ | <math>\textbf{(A)}\ 1011\qquad\textbf{(B)}\ \frac{1011}{2}\qquad\textbf{(C)}\ 2021\qquad\textbf{(D)}\ \frac{2021}{2}\qquad\textbf{(E)}\ 4042</math> | ||

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+ | [[G285 MC10A Problems/Problem 5|Solution]] |

## Revision as of 20:54, 11 May 2021

Posting here until I find a place for an upcoming mock I’m creating

## Problem 1

What is the smallest value of that minimizes ?

## Problem 2

Suppose the set denotes . Then, a subset of length is chosen. All even digits in the subset are then are put into group , and the odd digits are put in . Then, one number is selected at random from either or with equal chances. What is the probability that the number selected is a perfect square, given ?

## Problem 3

Let be a unit square. If points and are chosen on and respectively such that the area of . What is ?

## Problem 4

What is the smallest value of for which

## Problem 5

Let a recursive sequence be denoted by such that and . Suppose for . Let an infinite arithmetic sequence be such that . If is prime, for what value of will ?