Common difference of an Arithmetic Progression, whose 3^(rd) term is 5 and 7^(th) term is 9, is
Common difference of an Arithmetic Progression, whose 3rd term is 5 and 7th term is 9, is
A) 1
B) 2
C) 3
D) 4
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Correct option is (A) 1
We have \(a_3=5\;\&\;a_7=9\)
\(\therefore a+2d=5\) ______________(1)
& \(a+6d=9\) ______________(2) \((\because a_n=a+(n-1)d)\)
Subtract equation (1) from (2), we get
\((a+6d)-(a+2d)=9-5\)
\(\Rightarrow4d=4\)
\(\Rightarrow d=\frac44=1\)
\(\therefore a=5-2d\) (From (1))
\(=5-2=3\)
Hence, common difference of given arithmetic progression is d = 1.
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