Question

The 5th term of the Arithematic sequence is 9.its 9th term is 5.what is the common difference?what is the 14th term?

Answer 1

$T_n=a+(n-1)d$
1) $t_5=9$
$\Rightarrow 9=a+(5-1)d\Rightarrow a+4d=9\dots \dots \left(1\right)$
2) $t_9=5$
$\Rightarrow 5=a+(9-1)d\Rightarrow a+8d=5\dots \dots \left(2\right)$
(2) - (1) $(a+8d)-(a+4d)=5-9$
$\Rightarrow 4d=-4\Rightarrow d=-1$
Common difference =-1
$\therefore a=9-4(-1)=13T_{14}=a+(14-1)d=13+13(-1)=0$