Question

If the 3rd and the 9th term of an AP are 4 and -8 respectively, which term of this AP is zero?

Answer 1

$a_n=a+\left(n-1\right)d$

$a_3=4=a+2d$ $....\left(1\right)$

$a_9=-8=a+8d$ $....\left(2\right)$

$\therefore 4-2d=-8d-8$

$-2d+8d=-8-4$

$6d=-12$

$d=-2$

$a=4-2d$

$=4+4=8$

$a_n=0,a=8,d=-2$

$0=8+\left(n-1\right)\times \left(-2\right)$

$0=8-2n+2$

$2n=10$

$n=5$