Home › JEE Main › mathematics › Sequences and Series › For two positive numbers, the arithmetic mean eq…
For two positive numbers, the arithmetic mean equals the geometric mean if and only if:
Aone of them is zero
Btheir product is 1
Cthe two numbers are equal
Dthey are reciprocals
Answer & Solution
Correct answer: C. the two numbers are equal
By AM–GM, equality A.M. = G.M. holds exactly when the two numbers are equal.
Related questions
Sum of GP: 1 + 1/2 + 1/4 + ... to infinity =GP with first term 2, common ratio 3. Find 5th term.Sum of first 20 natural numbers:The 10th term of the AP 3, 7, 11, ... is:The AM-GM INEQUALITY for two POSITIVE numbers $a$ and $b$ states thatIf the AM and GM of two positive numbers are $5$ and $4$ respectively, the numbers areThree numbers are in AP. Their sum is $24$ and their product is $440$. Find the smallest oSum of the CUBES of the first $n$ natural numbers, $1^3 + 2^3 + \ldots + n^3$, equals