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  1. A number 15 is divided into 3 parts which are in Arithmetic Progression (A.P) and the sum of their squares is 83. What will be the smallest number?
    1. 5
    2. 3
    3. 6
    4. 8
Correct Option: B

Let us assume the second number is a and the difference between consecutive numbers is d.
According to Arithmetic progression,
First number = a - d
Second number = a
Third number = a + d
According to question,
Sum of the all three numbers = 15
a - d + a + a + d = 15
3a = 15
a = 5
Again according to given question,
sum of square of the 3 numbers = 83
(a - d) 2 + a 2 + (a + d) 2 = 83
apply the algebra formula
a 2 + d 2 - 2ad + a 2 + a 2 + d 2 + 2ad = 83
3a 2 + 2d 2 = 83
Put the value of a in above equation.
3 x 5 2 + 2d2 = 83
3 x 25 + 2d2 = 83
75 + 2d2 = 83
2d 2 = 83 - 75
2d 2 = 8
d 2 = 8/2
d 2 = 4
d = 2
Put the value of a and d in below equation.
First number = a - d = 5 - 2 = 3
Second number = a = 5
Third number = a + d = 5 + 2 = 7
The smallest number is 3.



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