Question

a=2, d=8,sn=90 find n and an

Answer 1

Step-by-step explanation:

Sn = 90

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

90 = n/2 [ 2 x 2 + (n - 1)8]

180/n = 4 + 8n - 8

180/n = 8n - 4

180 = 8n^2 - 4n

8n^2 - 4n - 180 = 0

2n^2 - n - 45 = 0

2n^2 - 10n + 9n - 45 = 0

2n( n - 5) + 9( n - 5) = 0

(2n + 9)(n - 5) = 0

n = -9/2 or n = 5

But n cannot be negative.

So, n = 5

an = a + (n - 1)d

a5 = 2 + (5-1)8

a5 = 2 + 4 x 8

a5 = 2 + 32 = 34

Hope This Helps You!

Answer 2

Answer:

n=12

Step-by-step explanation:

90=2+(n-1)8

90-2=8n-8

88=8n-8

8n=88+8

8n=96

n=96÷8=12

Sn=a+(n-1)d

this sum based on AP