Question

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

Answer 1

90=(n/2)(4+(n-1)8)
180=n(8n^2-4n)
8n^2-4n-180=0
n=5
an=34

Answer 2

Given :-

• a = 2
• d = 8
• Sn = 90

To Find :-

• n and an.

Solution :-

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

➜ 90 = n/2 [2 × 2 + (n - 1) × 8]

➜ 90 = n/2 [5 + 8n - 8]

➜ 90 = n/2 [8n - 4]

➜ 90 = 4n/2 [2n - 1]

➜ 90 = 2n [2n - 1]

➜ 4n² - 2n = 90

➜ 4n² - 2n - 90 = 0

➜ 2(2n² - n - 45) = 0

➜ 2n² - n - 45 = 0

➜ 2n² - 10n + 9n - 45 = 0

➜ 2n(n - 5) + 9(n - 5) = 0

➜ (n - 5) (2n + 9) = 0

➜ n = 5 (or) n = -9/2 (discarded)

➜ n = 5

an = a5

➦ a + 4d

➦ 2 + 4 × 8

➦ 2 + 32

➦ 34

Hence,

• n = 5

• an = 34