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Question
Write the next four terms of the following A.P. a+b,a−b,a−3b
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Solution
In the given progression is a+b,a−b,a−3b,......, the first term a1=a+b, second term a2=a−b and third term a3=a−3b. So, the difference between the two terms of the given progression is:
d=a2−a1=a−b−(a+b)=a−b−a−b=−2b
Therefore, the next four terms of the arithmetic progression are:
a4=a3−2b=a−3b−2b=a−5b
a5=a4−2b=a−5b−2b=a−7b
a6=a5−2b=a−7b−2b=a−9b
a7=a6−2b=a−9b−2b=a−11b
Hence, the next four terms are a−5b,a−7b,a−9b,a−11b.
d=a2−a1=a−b−(a+b)=a−b−a−b=−2b
Therefore, the next four terms of the arithmetic progression are:
a4=a3−2b=a−3b−2b=a−5b
a5=a4−2b=a−5b−2b=a−7b
a6=a5−2b=a−7b−2b=a−9b
a7=a6−2b=a−9b−2b=a−11b
Hence, the next four terms are a−5b,a−7b,a−9b,a−11b.
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