If every term of a $G.P.$ with positive terms is the sum of its two previous terms,then the common ratio of the series is

For a series $S = 1 - 2 + 3 - 4 + \dots$ up to $n$ terms,
Statement $-1$: The sum of the series is always dependent on the value of $n$,i.e.,whether it is even or odd.
Statement $-2$: The sum of the series is $-\frac{n}{2}$ when $n$ is any even integer.

If the roots of the equation ${x^3} - 12{x^2} + 39x - 28 = 0$ are in $A.P.$,then their common difference will be

If the first,second and last terms of an $A.P.$ are $a, b, 2a$ respectively,then its sum will be

Given $a_1, a_2, a_3, \dots$ form an increasing geometric progression with common ratio $r$ such that $\log_8 a_1 + \log_8 a_2 + \dots + \log_8 a_{12} = 2014$,then the number of ordered pairs of integers $(a_1, r)$ is equal to

If $s$ is the sum of an infinite $G.P.$ and $a$ is the first term,then the common ratio $r$ is given by: