The number of terms common to the two A.P.'s $3,7,11, \ldots ., 407$ and $2,9,16, \ldots . .709$ is

If the sum of $n$ terms of an $A.P.$ is $nA + {n^2}B$, where $A,B$ are constants, then its common difference will be

The sum of numbers from $250$ to $1000$ which are divisible by $3$ is

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 $n=1,2,3,4,5$

Let $S_n$ denote the sum of the first $n$ terms of an $A.P$.. If $S_4 = 16$ and $S_6 = -48$, then $S_{10}$ is equal to

For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,

Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd. 

Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer