Question

Which term of the AP 3, 10, 17 ...... will be 84 more than its ${13}^{th}$ term? [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

$a=3,d=7,a_{13}=a+12d$

$a+(n-1)d=84+a_{13}$

$\Rightarrow 3+(n-1)7=84+3+12\left(7\right)$

$\Rightarrow 3+7n-7=84+3+84$

$\Rightarrow 7n=171+4$

$\Rightarrow n=\frac{175}{7}=25$

$25th$ term.