If $a, b, c, d, e$ are in an arithmetic progression,then what is the value of $a - 4b + 6c - 4d + e$?

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$,then $8 \sigma^2$ is equal to

If the sum of $n$ terms of the sequence $2, 5, 8, 11, \dots$ is $60100$,then $n = \dots$

Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$

If the sum of $n$ terms of an arithmetic progression is $3n^2 + 5n$ and $T_m = 164$,then $m = \dots$

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