In an A.P if third term is 7 and seventh term is 15, then first term i

1.	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
Answer» 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. Correct option is 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

Answer»

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.

Correct option is D) 3