Question

given a=2,d=8,Sn=90​

Answer 1

Answer:

Sn = n/2(2a + (n-1)d)

90 = n/2(4+(n-1)8)

180=n(4+8n-8)

180 = 8n^2 - 4n

8n^2-4n-180=0

by solving this quadrti equation you will get the answer.

if you want me to solve the equation too then inform me through comments.

Hope it helped you

Answer 2

Answer:-

The sum of n terms of an AP is given by :

$\small\sf{Sn=\frac{n}{2}(2a+(n-1)d)}$

$\small\sf{90=\frac{n}{2}(2(2)+(n-1)8)}$

$\small\sf{90=\frac{n}{2}(4+(n-1)8)}$

$\small\sf{90=\frac{n}{2}(8n-4)}$

$\small\sf{90={4n}^{2}-2n}$

$\small\sf{{2n}^{2}-n-45=0}$

$\small\sf{{2n}^{2}-10n+9n-45=0}$

$\small\sf{2n(n-5)+9(n-5)=0}$

$\small\sf{(2n+9)(n-5)=0}$

$\small\sf{n-5=0}$

$\small\sf{n=5}$

━━━━━━━━━━━━━━━

$\small\sf{an=a+(n-1)d}$

$\small\sf{a5=2+(5-1)(8)}$

$\small\sf{2+32}$

$\small\sf{34}$

$\small\sf{an=34}$