An arithmetic progression has first term and common difference
MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
An arithmetic progression has first term 20 and common difference −3.
(i) Explain whether the successive terms of this progression increase or decrease as n increases.
(ii) Without performing detailed calculations, justify whether the 10th term will be positive or negative.
(iii) Describe how the sign of the common difference influences the long-term behaviour (very large n) of the terms in any AP.