Question

AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20 is 3, 7, 11, 15, .......
If true then enter $1$ and if false then enter $0$

Answer 1

Let $a$ and $d$ be the first term and common difference of AP respectively.
Now,
$a_5=a+4d=19$ ...(1)
$a_{13}-a_8=(a+12d)-(a+7d)=20$
$\Rightarrow 5d=20$
$\Rightarrow d=4$
On substituting the value of d in (1), we get
$a+4\times 4=19$
$\Rightarrow a=3$
Therefore the AP is
$a,a+d,a+2d,a+3d...$
$3,7,11,\mathrm{15...}$