Question

Which term of the AP 12, 7, 2, -3 is -98.

Answer 1

$\colorbox{black}{\color{green}{solution}}$


AP : 12, 7 , 2 , - 3 , ........

Common difference (d) = 7 - 12 = - 5

$\underline {which \: term \: of \: the \: ap \: is \: ( - 98)}$
$let \\ \\ a_n = - 98 \\ \\ then \\ \\ \: \colorbox{yellow}{ an = a + (n - 1)d} \\ \\ \implies - 98 = 12 + (n - 1) \times ( - 5) \\ \\ \implies - 98 = 12 - 5n + 5 \\ \\ \implies - 5n = - 98 - 17 \\ \\ \implies \: n = \frac{ - 115}{ - 5} \\ \\ \implies \: n = 23$


$\colorbox{yellow}{\color{red}so \: ( - 98) \: is \: the \: 23rd \: term \: of \: the \: ap}$