Question

3) The sum of fourth and eight term of A. P. IS 54 and their product is 665 . Find the sum
Of first fifty terms.
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Answer 1

Answer:

256 is your answer hope ao yo liked it i may be wrong

Answer 2

Answer:

5250

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        [neglect - ve]

 thus, a = 27 - 5(4) = 7

 ∴ Sum of 1st 50 terms is

                 = (50/2) [2(7) + 49(4)]

                 = 25[14 + 196]

                 = 5250