n 3. Suppose that 81, 82, 83,... is a strictly increas subsequences 81, 82, 8831... and Bài th arithmetic progressions. Prove that the sequence a

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 48E
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Problem 3. Suppose that 81, 82, 83,... is a strictly increasing sequence of positive integers such
that the subsequences
801, 82, 802... and 881+1, 82+1, 883+1,...
are both arithmetic progressions. Prove that the sequence 81, 82, 83,... is itself an arithmetic pro-
gression.
Transcribed Image Text:Problem 3. Suppose that 81, 82, 83,... is a strictly increasing sequence of positive integers such that the subsequences 801, 82, 802... and 881+1, 82+1, 883+1,... are both arithmetic progressions. Prove that the sequence 81, 82, 83,... is itself an arithmetic pro- gression.
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