If the geometric mean of two positive numbers is $6$ and their arithmetic mean is $6.5$,then the numbers are.........

If $A, G,$ and $H$ are the arithmetic mean,geometric mean,and harmonic mean of two given numbers respectively,then which of the following is true?

Let $A_1, G_1, H_1$ be the arithmetic,geometric,and harmonic means of two distinct positive numbers. For $n \geq 2$,let $A_n, G_n, H_n$ be the arithmetic,geometric,and harmonic means of $A_{n-1}$ and $H_{n-1}$ respectively. Which of the following statements is true?

If $a_1, a_2, \dots, a_n$ are positive real numbers such that $a_1 \cdot a_2 \cdot \dots \cdot a_n = 1$,then their sum is:

The first term of an arithmetic progression is $1$. If the second,tenth,and thirty-fourth terms form a geometric progression,then the common difference of the arithmetic progression is:

For two positive numbers $a$ and $b$,if $a, b$ and $\frac{1}{18}$ are in a geometric progression,while $\frac{1}{a}, 10$ and $\frac{1}{b}$ are in an arithmetic progression,then $16a + 12b$ is equal to $.........$.