WebSolution. Let the numbers be (a – 3d), (a – d), (a + d), (a + 3d), Then. Sum = 20. ⇒ (a – 3d) + (a – d) + (a + d) + (a + 3d) = 20. ⇒ 4a = 20. ⇒ a = 5. Sum of the squares = 120. ( a – 3. WebLet the four numbers in AP be,a−3d,a−d,a+d,a+3dTheir sum => 4a=20=> a=5Sum of their squares = (a−3d) 2+(a−d) 2+(a+d) 2+(a+3d) 2=120=> 4a 2+20d 2=120On putting value of. WebFind four numbers in AP whose sum is 20 and the sum of whose squares is 120 About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How.
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Web4a = 20 . a = 5. Sum of the squares = 120 (a − 3 d) 2 + (a − d) 2 + (a + d) 2 + (a + 3 d) 2 = 120. 4 a 2 + 20 d 2 = 120. a 2 + 5 d 2 = 30. 25 + 5 d 2 = 30 [Since, a = 5] 5 d 2 = 5 . d = ±. WebMinimizing Sum: Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum. The sum of two numbers is five. The sum of the squares of. WebFind four numbers in AP whose sum is 20 and the sum of whose squares is 120. Arithmetic Progression class 10. #arithmeticprogression #arithmeticprogressioncl... WebAs, given in the question that the sum of four terms of the A.P is 20. So, ( a − 3 d) + ( a − d) + ( a + d) + ( a + 3 d) = 20. So, on solving the above equation. We get, ⇒ 4. WebWe can take the no. As (a-2d),(a-d),(a+d),(a+2d) As their sum is 20 (a-3d)+(a-d)+(a+d)+(a+3d)=20 4a=20 a=5 Then its mentioned that the sum of squares is 120 (a. WebSolution. Let the four numbers in A.P be and ( a - 3 d), ( a - d), ( a + d) and ( a + 3 d). Then Then, ( a - 3 d) + ( a - d) + ( a + d) + ( a + 3 d) = 20. ⇒ 4 a = 20. ⇒ a = 5. It is given that. (. WebSum of the squares = 120 `(a – 3d)^2 + (a – d)^2 + (a + d)^2 + (a + 3d)^2 = 120` `⇒ 4a^2 + d^2 = 120` `⇒ a^2 + 5d^2 = 30` ⇒ 25 + 5d2 = 30 [∵ a = 5] ⇒ 5d2 = 5 ⇒ d = ± 1. If d = 1,. WebLet the four numbers in A.P be a-3d, a-d,a+d,a+3d. ---- (1) Given that Sum of the terms = 20. = (a-3d) + (a-d) + (a+d) + (a+3d) = 20. 4a = 20. a = 5. ---- (2) Given that. WebCALCULATION: Given: The four numbers are in AP such that their sum is 20 and the sum of their squares is 120. Let (a - 3d), (a - d), (a + d) and (a + 3d) be the required four terms. ∵.
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