Question

four number are in ap if their total is 20 and their sequre is 120 what is the number

Answer 1

let four number in ap are (a-3d),(a-d), (a+d) and (a+3d).Then
Their sum = 20
a-3d+a-d+a+d+a+3d = 20
4a = 20
a= 5
You write mistake , there should be sum of square .
so
(a-3d)^2 +(a-d)^2 +(a+d)^2 +(a+3d)^2 =120
a^2-6ad+9d^2 + a^2-2d+d^2 +a^2+2d+d^2 +a^2+6ad+9d^2 = 120
or, 4a^2+20d^2= 120
Since a = 5
so ,
4×25+20d^2 = 120
100+20d^2 = 120
20d^2= 20
d= 1
Now four numbers should be (5-3×1),(5-1), (5+1) and (5+3×1)
i.e 2,4,6,8 .hope it helps you