Question

which term of the arithematic progression, -12, -9,-6,... is 0​

Answer 1

$\Large \blue{ Answer:}$

$■ \: \bf {a_5 = 0}$

$■ \: \tt {The\: fifth \: term \: of \: the\: given}$ $\tt {arithmetic\: progression \:will \: be \: 0.}$

$\Large \blue{Step-by-step \: explanation:}$

$a = a_1 = -12 \\ a_2 = -9 \\ a_3 = -6 \\a_n = 0$

$d = a_n - a_{n-1}$

$\therefore \: d = a_3 - a_2 = -6 -(-9) = -6+9 = \bold 3$

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

$\therefore\: 0 = -12 + (n - 1) 3$

$\therefore \: 12 = 3n - 3$

$\therefore \: 12+3 = 3n$

$\therefore \: 15 = 3n$

$\therefore \: n = \large \frac{15}{3}$

$\Longrightarrow \: \pink{\fbox{n = 5}}$

$\bf \orange{Hence \: the\: fifth \: term \: of \: the\: given}$ $\bf \orange {arithmetic\: progression \:will \: be \: 0.}$