Difference between revisions of "G285 2021 MC-IME I"

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==Problem 1==
 
==Problem 1==
Let a recursive sequence <math>a_n</math> be defined such that <math>a_1=20</math>, and <math>a_n=16a_{n-1}+4</math>. Find the last <math>4</math> digits of <cmath>\sum_{i=1}^{100} a_i</cmath>
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Let a recursive sequence <math>a_n</math> be defined such that <math>a_1=20</math>, and <math>a_n=16a_{n-1}+4</math>. Find the last <math>3</math> digits of <cmath>\sum_{i=1}^{100} a_i</cmath>
  
 
[[G285 2021 MC-IME I Problem 1|Solution]]
 
[[G285 2021 MC-IME I Problem 1|Solution]]

Revision as of 18:36, 10 June 2021

Problem 1

Let a recursive sequence $a_n$ be defined such that $a_1=20$, and $a_n=16a_{n-1}+4$. Find the last $3$ digits of \[\sum_{i=1}^{100} a_i\]

Solution

Problem 2

If the number $abcd_{11}$ is a palindrome in base $7$, and $dcba$ expressed in base $10$ does not begin with a nonzero digit, find the difference between the largest and smallest possible sum of $a+b+c+d$.

Solution