Question

sum of 4th and 8th term of an AP is 54 and their prosuct is 665 . Find sum of first 30 terms of an AP​

Answer 1

Answer:

As it's given

S4+S8 = 665

2 (2a+3d ) + 4(2a+7d )= 665

4a+6d+8a+28d =665

12a+34d=665------------@

Solve it further

Answer 2

Answer:

1950

Step-by-step explanation:

According to the question, sum of 4th and 8th terms is 54

⇒ (a + 3d) + (a + 7d) = 54

⇒ 2a + 10d = 54

⇒ a + 5d = 27    

⇒ a = 27 - 5d    

Their product = 665

⇒ (a + 3d)(a + 7d) = 665

⇒ (27-5d + 3d)(27-5d + 7d) = 665

⇒ (27 - 2d)(27 + 2d) = 665

⇒ (27)² - (2d)² = 665

⇒ 729 - 4d² - 665

⇒ 64 = 4d²

⇒ 16 = d²

⇒ 4 = d      

 thus, a = 27 - 5(4) = 7

 ∴ Sum of 1st 30 terms is

                 = (30/2) [2(7) + 29(4)]

                 = 15[14 + 116]

                 = 1950