If $a,b,c,d,e$ are in $A.P.$ then the value of $a + b + 4c$ $ - 4d + e$ in terms of $a$, if possible is
$4a$
$2a$
$3$
None of these
The ratio of the sums of $m$ and $n$ terms of an $A.P.$ is $m^{2}: n^{2} .$ Show that the ratio of $m^{ th }$ and $n^{ th }$ term is $(2 m-1):(2 n-1)$
Given that $n$ A.M.'s are inserted between two sets of numbers $a,\;2b$and $2a,\;b$, where $a,\;b \in R$. Suppose further that ${m^{th}}$ mean between these sets of numbers is same, then the ratio $a:b$ equals
The four arithmetic means between $3$ and $23$ are
In $\Delta ABC$, if $a, b, c$ are in $A.P.$ (with usual notations), identify the incorrect statements -
The sum of the first and third term of an arithmetic progression is $12$ and the product of first and second term is $24$, then first term is