alleryFor two positive real numbers, how does the arithmetic mean compare with the geometric mean?
AA is smaller or equal
BA is always smaller
CA is always unequal
DA is greater or equal
Answer & Solution
Correct answer: D. A is greater or equal
1. Write A for the arithmetic mean and G for the geometric mean.
2. Their difference works out to a square divided by two.
3. A square is never negative, so that difference is never negative.
4. From this we obtain the relationship A is greater than or equal to G.
_Source: syllabus Mathematics, Ch 8 'Sequences and Series'_
Keep practising Sequences and Series
Browse all Sequences and Series questions for JEE Advanced, or explore more Mathematics topics.
Related questions
Complete the definitionsWhich is largerSequence or seriesWhich ones belongArithmetic or geometricInserting 4, 16 and 64 between 1 and 256 makes the resulting sequence a:For a geometric progression with first term 2 and ratio 2, the sum of ten terms is:If the geometric mean of two positive numbers is 8, their product must be: