Question

If the $3^{rd}$ and $9^{th}$ term of an AP are 4 and -8 respectively, which term of this AP is zero? [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

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

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

Subtracting (2) from (1)

a + 2d - a - 8d = 4 - (-8)

$\Rightarrow -6d=12$

$\Rightarrow d=-2$

Substituting in (1)

$a+2(-2)=4\Rightarrow a=4+4=8$

Let
$a_n=0$

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

$\Rightarrow 0=8+(n-1)(-2)$

$\Rightarrow 0=8-2n+2$

$\Rightarrow 2n=10$

$\Rightarrow n=5$