10

Part of 2016 AIME Problems

Problems(2)

Arithmetico-geometric... sequence?

Source: 2016 AIME I #10

A strictly increasing sequence of positive integers

a_1, a_2, a_3, \ldots

has the property that for every positive integer

k

, the subsequence

a_{2k-1}, a_{2k}, a_{2k+1}

is geometric and the subsequence

a_{2k}, a_{2k+1}, a_{2k+2}

is arithmetic. Suppose that

a_{13} = 2016

a_1

AIME2016 AIME ISequence

We meet again...

Source: 2016 AIME II #10

ABC

is inscribed in circle

\omega

P

Q

\overline{AB}

AP<AQ

CP

CQ

\omega

S

T

C

), respectively. If

AP=4,PQ=3,QB=6,BT=5,

AS=7

ST=\frac{m}{n}

m

n

are relatively prime positive integers. Find

m+n

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