Grove HSC 3U EX 8.5 Q8

 

Formula is $S_n={n\over 2} (2a+(n-1)d)$

$a=5$

$d=4$

$S_n=152$

$ S_n= {n\over 2} (2a+(n-1)d)$

$ S_n= {n\over 2} (2(5)+4(n-1))$

$ S_n= {n\over 2}(10+4n-4)$

$S_n=2n^2+3n$

$\therefore 2n^2+3n=152$

$2n^2+3n-152=0$

$n={-3\pm \sqrt{3^2-4(2)(-152)} \over 2(2)}$

$n={-3\pm \sqrt{9+1216} \over 4}$

$n={-3\pm \sqrt{1225} \over 4}$

$n={-3\pm 35 \over 4}$

$n={-3+ 35 \over 4}, {-3- 35 \over 4}$

$n=8, -19/2$

Hence since $n$ is whole number 

$n=8$.

:-) JH 2016