MathDB

A sequence of positive integers with

a_1=1

and

a_9+a_{10}=646

is formed so that the first three terms are in geometric progression, the second, third, and fourth terms are in arithmetic progression, and, in general, for all

n\ge1

, the terms

a_{2n-1}

a_{2n}

a_{2n+1}

are in geometric progression, and the terms

a_{2n}

a_{2n+1}

, and

a_{2n+2}

are in arithmetic progression. Let

a_n

be the greatest term in this sequence that is less than 1000. Find

n+a_n

Problem Statement