There are $n$ arithmetic means between $7$ and $71$. If the $5^{th}$ arithmetic mean is $27$,then $n = ......$

If the sum of a certain number of terms of the $A.P.$ $25, 22, 19, \ldots$ is $116$,find the last term.

If $a\left(\frac{1}{b}+\frac{1}{c}\right), b\left(\frac{1}{c}+\frac{1}{a}\right), c\left(\frac{1}{a}+\frac{1}{b}\right)$ are in $A.P.$,prove that $a, b, c$ are in $A.P.$

If the sum of $n$ terms of the sequence $2, 5, 8, 11, \dots$ is $60100$,then $n = \dots$

If ${a^2}, {b^2}, {c^2}$ are in $A.P.$,then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ will be in

If $a_1, a_2, a_3, \dots, a_{21}$ are in $A.P.$ and $a_3 + a_5 + a_{11} + a_{17} + a_{19} = 10$,then the value of $\sum_{r=1}^{21} a_r$ is: