Question

$1^{st}51$ terms of the AP whose $2^{nd}$ term is $2$ and $4^{th}$ is $8$

Answer 1

2nd term$=2$

4th term$=8$

$a+(n-1)d=2$

$\Rightarrow a+a=2$(2nd term)-------------(1)

$a+(n-1)d=8$

$\Rightarrow a+3d=8$-------------------(2)

$a+d=2$

$a+3d=8$

On substraction:- $-2d=-6$

$\Rightarrow d=3$

Putting $d$ in Equation(1)

$a=-1$

So, 51st term$=(-1)+(51-1)3=149$