Sum = Product

Algebra Level 1

Suppose that a , b a,b and c c are consecutive (positive, integer valued) terms in an arithmetic sequence, and that a b c = a + b + c abc = a+b+c .

Find a + b + c a+b+c .


The answer is 6.

Samir Betmouni by Samir Betmouni , 51, United Kingdom

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1 solution

Marta Reece
Dec 23, 2017

a = b − x , c = b + x a=b-x, c=b+x

a b c = b ( b + x ) ( b − x ) = a + b + c = b − x + b + b + x = 3 b abc=b(b+x)(b-x)=a+b+c=b-x+b+b+x=3b

( b + x ) ( b − x ) = 3 = 1 × 3 (b+x)(b-x)=3=1\times3

b = 2 , x = 1 b=2, x=1

a + b + c = 3 b = 6 a+b+c=3b=\boxed6

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