Question

Given a=2, d=8, Sn=90, find n and An?

Answer 1

Sn = (n/2)(2a+(n-1)d) 

90 = (n/2)(4+(n-1)8) 

180 = n(8n-4) 

180 = 8n^2-4n 

8n^2-4n-180 = 0 

n=5 

An = 2+4*8=34

Answer 2

Sn=90, d=8, a=2
  
Sn =n/2[2a+(n-1) x d]
⇒ 90= n/2[2x2+(n-1)x 8]
⇒90 = n/2[4+8n-8]
⇒90 = n/2x2[2+4n-4] [then 2 and 2 will be cancel]
⇒90 = 2n +4n²-8n
⇒90 = -6n +4n²
⇒4n²-6n -90 =0
⇒ 4n² - 20n+18n -90=0
⇒2n(2n-10)+9(2n-10) =0
⇒(2n+10) (2n+9)
n=-9/2 ,5
 lets take n=5
an=2+(n-1)x d
a5=2 + (5-1)x 8
= 2+4 x 8
= 2+32
=34

so,the an=34 and n=5