G285 2021 MC-IME I

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 $4$ 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

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G285 2021 MC-IME I

Problem 1

Problem 2