Question

find four numbers in AP whose sum is 20 and sum of whose square is 150



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Answer 1

Answer:

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Answer 2

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) = 20

4a = 20

  a = 5.    ---- (2)

Given that sum of squares of the term = 150.

= (a-3d)^2 + (a-d)^2 + (a+d)^2 + (a+3d)^2 = 150

=(4a)² + (d)² = 150

=>a²+d² = 37.5

=> 25+5d²= 37.5[Since,a=5]

=> 5d² =12.5

=>d² = 2.5

=> d=±1.5

the four numbers are:

Taking d = 1                  

(a – 3d), (a – d), (a + d), (a + 3d)                 

= (5 – 4.5), (5 – 1.5), (5 + 1.5), (5 + 3)                 

= 0.5, 3.5, 6.5, 8

Taking d = -1  

=(a – 3d), (a – d), (a + d), (a + 3d)                 

=[5 - (-3)], [5 - (-1.5)], [5 + (-1.5)], [5 +(-4.5)]   

= (5 + 3), (5 + 1.5), (5 - 1.5), (5 - 4.5)   

= 8, 6.5, 3.5, 0.5