Question

In an AP the sum of 4 terms is 20 and sum of their squares is120

Answer 1

Answer:

Step-by-step explanation:

Let 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) = 204a = 20  a = 5.    ---- (2)Given that sum of squares of the term = 120.= (a-3d)^2 + (a-d)^2 + (a+d)^2 + (a+3d)^2 = 120= (a^2 + 9d^2 - 6ad) + (a^2+d^2-2ab) + (a^2+d^2+2ad) + (a^2+9d^2+6ad) = 120= 4a^2 + 20d^2 = 120Substitute a = 5 from (2) .4(5)^2 + 20d^2 = 120100 + 20d^2 = 12020d^2 = 20d = +1 (or) - 1..Substitute a = 5 and d = 1 in (1), we get a - 3d, a-d, a+d, a+3d = 2,4,6,8.

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Answer 2

HERE IS THE SOLUTION

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