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  4. The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

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Q. The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

BITSATBITSAT 2016

Solution:

Let the progression be $a, a+d, a+2 d$,
Then $x_{4}=3 x_{1}$
$ \Rightarrow a+3 d=3 a$
$ \Rightarrow 3 d=2 a \ldots$ (i)
Again $x_{7}=2 x_{3}+1$
$\Rightarrow a+6 d=2(a+2 d)+1 $
$\Rightarrow 2 d=a+1 \ldots$ (ii)
Solving (i) and (ii), we get
$a =3, d =2$