In an A.P if third term is 7 and seventh term is 15, then first term is A) 2 B) 0 C) 5 D) 3
In an A.P if third term is 7 and seventh term is 15, then first term is
A) 2
B) 0
C) 5
D) 3
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Correct option is (D) 3
We have \(a_3=7\;\&\;a_7=15\)
\(\therefore a+2d=7\) ________________(1)
& \(a+6d=15\) ________________(2) \((\because a_n=a+(n-1)d)\)
Multiply equation (1) by (3), we get
\(3a+6d=21\) ________________(3)
Subtract equation (2) from (3), we get
\((3a+6d)-(a+6d)=21-15\)
\(\Rightarrow2a=6\)
\(\Rightarrow a=\frac62=3\)
Hence, first term of A.P. is 3.
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