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
Statement $-1$ is true, statement $-2$ is true but statement $-1$ is not the correct explanation for statement $-2$
Statement $-1$ is true, statement $-2$ is false
Statement $-1$ is false, statement $-2$ is true
Both statements are true, and statement $-1$ is the true explanation of statement $-2$
Find the $7^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=\frac{n^{2}}{2^{n}}$
The number of terms in an $A .P.$ is even ; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2}$ , then the number of terms in the $A.P.$ is
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
If the sides of a right angled traingle are in $A.P.$, then the sides are proportional to
If $x,y,z$ are in $A.P.$ and ${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$ and ${\tan ^{ - 1}}z$ are also in other $A.P.$ then . . .