If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =
$\frac{2}{{{a_{m + k}} + {a_{m - k}}}}$
$\frac{{{a_{m + k}} - {a_{m - k}}}}{2}$
$\frac{{{a_{m + k}} + {a_{m - k}}}}{2}$
None of these
The sum of the first four terms of an $A.P.$ is $56 .$ The sum of the last four terms is $112.$ If its first term is $11,$ then find the number of terms.
If $\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}$ are in an $A.P.$ and $\log _e \mathrm{a}-$ $\log _e 2 b, \log _e 2 b-\log _e 3 c, \log _e 3 c-\log _e a$ are also in an $A.P,$ then $a: b: c$ is equal to
Find the sum of all two digit numbers which when divided by $4,$ yields $1$ as remainder.
Find the $9^{\text {th }}$ term in the following sequence whose $n^{\text {th }}$ term is $a_{n}=(-1)^{n-1} n^{3}$
If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is