the sum of four no. in AP is 26 and the sum of their square is 214 find the numbers
Answers
Here is the answer in the picture.
p.s. : I'm new here and I find it very difficult to write the sum in text. so, I've attached the picture. Hope you find it helpful. :)
Given : sum of four no. in AP is 26 and the sum of their square is 214
To find : the numbers
Solution:
Let say four numbers in AP are
a - 3d , a - d , a + d , a + 3d
Sum of 4 numbers
= a - 3d + a - d + a + d + a + 3d
= 4a
4a = 26
=> a = 26/4
=> a = 13/2
(a - 3d)² + (a - d)² + (a + d)² + (a + 3d)² = 214
=> a² + 9d² - 6ad + a² + d² - 2ad + a² + 9d² + 6ad + a² + d² + 2ad = 214
=> 4a² + 20d² = 214
=> 4(13/2)² + 20d² = 214
=> 169 + 20d² = 214
=> 20d² = 45
=> 4d² = 9
=> d² = 9/4
=> d = ± 3/2
a - 3d , a - d , a + d , a + 3d
a = 13/2 , d = 3/2
=> 2 , 5 , 8 , 11
a = 13/2 , d = -3/2
11 , 8 , 5 , 2
Four numbers are 2 , 5 , 8 & 11
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