Three positive numbers are in arithmetic progression (a. p). the sum of the squares of the three numbers is 155. while the sum of the numbers is 21. if the common difference is positive. find the values of x and y

The required arithmetic sequence will be 5, 7, and 9 if the sum of the squares of the three numbers is 155. while the sum of the numbers is 21

Let the three positive numbers be a-d, a and a + d

If the sum of the numbers is 21, this means that a-d+a+a+d = 21

3a -d + d = 21

3a = 21

a = 21/3

a = 7

The sequence of numbers will be 7-d, 7 and 7+d

If the squares of the three numbers is 155, hence;

Hence the required arithmetic sequence will be 5, 7 and 9

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(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18