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Arithmetic Progressions

Question
CBSEENMA10007449

Which of the following are APs? If they form an AP, find the common difference d and write three more terms.

negative 1 half comma space minus 1 half space. space minus 1 half space. negative 1 half space comma.....

Solution
negative 1 half comma space minus 1 half space. space minus 1 half space. negative 1 half space comma.....
straight a subscript 2 minus straight a subscript 1 equals negative 1 half comma space minus open parentheses negative 1 half close parentheses space equals negative 1 half plus 1 half equals 0
straight a subscript 3 minus straight a subscript 2 equals negative 1 half minus open parentheses negative 1 half close parentheses equals negative 1 half plus 1 half equals 0
straight a subscript 4 minus straight a subscript 3 equals negative 1 half space minus open parentheses negative 1 half close parentheses equals negative 1 half plus 1 half equals 0

i.e., ak + 1 – ak is the same every time. So, the given list of numbers forms an A .P. with the common difference d = 0.
The next three terms are :


minus 1 half plus 0 equals negative 1 half comma space plus negative 1 half space plus space 0 space equals space minus 1 half
and space space space minus 1 half space plus 0 equals space minus 1 half