Question

the sum of the three consecutive numbers in A.P.is 21 and their product is 231.find the numbers

Answer 1

Let the numbers be a-d, a and a+d.
Then by the given condition, (a-d)+a+(a+d)=21 implies 3a=21 implies a=7
Again, (a-d)a(a+d)=231
or, (7-d)*7*(7+d)=231
or, 49-d^2=33 oe, d^2=16, or d=+4 or -4
Accordingly the series is 3,7,11 or 11,7,3