Let three real numbers a , b , c be in arithmetic progression and a + 1 , b , c + 3 be in geometric progression. If a 10 and the arithmetic mean of a , b and c is 8, then the cube of the geometric m

Question

Let three real numbers a , b , c be in arithmetic progression and a + 1 , b , c + 3 be in geometric progression. If a > 10 and the arithmetic mean of a , b and c is 8, then the cube of the geometric mean of a , b and c is

TestHub · Accepted Answer

​ 2 b = a + c , b 2 = ( a + 1 ) ( c + 3 ) 3 a + b + c ​ = 8 → b = 8 , a + c = 16 64 = ( a + 1 ) ( 19 − a ) = 19 + 18 a − a 2 a 2 − 18 a − 45 = 0 → ( a − 15 ) ( a + 3 ) = 0 , ( a > 10 ) a = 15 , c = 1 , b = 8 ( ( ab c ) 1/3 ) 3 = ab c = 120 ​

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