Matematické Fórum

stuart clark · 12. 02. 2012 17:50

Suppose that $s_{1}, s_{2}, s_{3}, . . .$ is a strictly increasing sequence of positive integers such that the

subsequences $Ss_{1} , Ss_{2} , Ss_{3} , . . .$ and $Ss_{1}+1, Ss_{2}+1, Ss_{3}+1, . . .$ are both arithmetic

progressions. Prove that the sequence $s_{1}, s_{2}, s_{3}, . . .$ is itself anarithmetic progression.

check_drummer · 12. 02. 2012 22:30

For all: pay attention on the progression:
$Ss_{1}+1, Ss_{2}+1, Ss_{3}+1, . . .$
From the picture it seems like "+1" is not in the index but looking at the latex expression it indeed is (which was expected from the nature of the problem).

stuart clark · 26. 02. 2012 05:59

stuart clark napsal(a):
Suppose that $s_{1}, s_{2}, s_{3}, . . .$ is a strictly increasing sequence of positive integers such that the

subsequences $Ss_{1} , Ss_{2} , Ss_{3} , . . .$ and $Ss_{1+1}, Ss_{2+1}, Ss_{3+1}, . . .$ are both arithmetic

progressions. Prove that the sequence $s_{1}, s_{2}, s_{3}, . . .$ is itself anarithmetic progression.

edited.

Matematické Fórum

#1 12. 02. 2012 17:50

arithmetic progression

#2 12. 02. 2012 22:30

Re: arithmetic progression

#3 26. 02. 2012 05:59

Re: arithmetic progression

stuart clark napsal(a):

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