Question

Consider the arithmetic sequence 11, 19, 27, 35, ....
The sum of the first n terms is 2090. Find the value of n.​

Answer 1

Step-by-step explanation:

Sn=2090

d=a2-a1

=19-11=8

a1=11

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

2090=n/2(2*11+(n-1)8)

4180=n(22+8n-8)

4180=n(14+8n)

4180=14n+8n^2

-8n^2-14n+4180=0

8n^2+14n-4180=0

Use duscriminant fornula of quardic equation

D=b^2-4ac

when D=0 nd D>0 then find n

n = x+-√D/2a