The four arithmetic means between $3$ and $23$ are
$5, 9, 11, 13$
$7, 11, 15, 19$
$5, 11, 15, 22$
$7, 15, 19, 21$
If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and $a,\;b,\;c$ are in $G.P.$, then $x,\;y,\;z$ will be in
Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is
If the ratio of the sum of $n$ terms of two $A.P.'s$ be $(7n + 1):(4n + 27)$, then the ratio of their ${11^{th}}$ terms will be
If ${S_k}$ denotes the sum of first $k$ terms of an arithmetic progression whose first term and common difference are $a$ and $d$ respectively, then ${S_{kn}}/{S_n}$ be independent of $n$ if
A manufacturer reckons that the value of a machine, which costs him $Rs.$ $15625$ will depreciate each year by $20 \% .$ Find the estimated value at the end of $5$ years.