14

Part of 2009 AIME Problems

Problems(2)

Minimum value of a sum

Source: 2009 AIME I #14

For t \equal{} 1, 2, 3, 4, define \displaystyle S_t \equal{} \sum_{i \equal{} 1}^{350}a_i^t, where

a_i \in \{1,2,3,4\}

. If S_1 \equal{} 513 and S_4 \equal{} 4745, find the minimum possible value for

S_2

linear algebramatrixmodular arithmeticAMC

Sequence with Square Root

Source: AIME 2009II Problem 14

(a_n)

satisfies a_0 \equal{} 0 and \displaystyle a_{n \plus{} 1} \equal{} \frac85a_n \plus{} \frac65\sqrt {4^n \minus{} a_n^2} for

n\ge0

. Find the greatest integer less than or equal to

a_{10}

trigonometryinductionabsolute valueAMC