Question

In an AP

Given a = 2 ; d = 8 ; Sn = 90

Find n and an.​

Answer 1

Solution :-

Given :

• a = 2
• d = 8
• Sn = 90

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

Answer 2

Answer:

$n = 5 \\ an = 34$