Question

Question 3 (vi)
In an AP:
(vi) Given a = 2, d = 8, $S_n=90$, find n and $a_n$.

Answer 1

$Giventhat,a=2,d=8,S_n=90As{S}_n=\frac{n}{2}[2a+(n-1\left)d\right]90=\frac{n}{2}[2a+(n-1\left)d\right]\Rightarrow 180=n(4+8n-8)=n(8n-4)=8n^2-4n\Rightarrow 8n^2-4n-180=0\Rightarrow 2n^2-n-45=0\Rightarrow 2n^2-10n+9n-45=0\Rightarrow 2n(n-5)+9(n-5)=0\Rightarrow (2n+9)(n-5)=0So,n=5\left(asitisapositiveinteger\right)\therefore a_5=2+8\times 4=34$