The number of $5 -$tuples $(a, b, c, d, e)$ of positive integers such that
$I.$ $a, b, c, d, e$ are the measures of angles of a convex pentagon in degrees
$II$. $a \leq b \leq c \leq d \leq e$
$III.$ $a, b, c, d, e$ are in arithmetic progression is
$35$
$36$
$37$
$126$
The sums of $n$ terms of two arithmatic series are in the ratio $2n + 3:6n + 5$, then the ratio of their ${13^{th}}$ terms is
If $a,\;b,\;c$ are in $A.P.$, then $\frac{1}{{bc}},\;\frac{1}{{ca}},\;\frac{1}{{ab}}$ will be in
The Fibonacci sequence is defined by
$1 = {a_1} = {a_2}{\rm{ }}$ and ${a_n} = {a_{n - 1}} + {a_{n - 2}},n\, > \,2$
Find $\frac{a_{n+1}}{a_{n}},$ for $n=1,2,3,4,5$
$8^{th}$ term of the series $2\sqrt 2 + \sqrt 2 + 0 + .....$ will be
If $\frac{1}{{b - c}},\;\frac{1}{{c - a}},\;\frac{1}{{a - b}}$ be consecutive terms of an $A.P.$, then ${(b - c)^2},\;{(c - a)^2},\;{(a - b)^2}$ will be in