If $k+1, 8, k+9$ are three consecutive terms of an $A.P.$,then $k = \ldots$

Which term of the $A.P.$ $83, 77, 71, \ldots$ is its first negative term (in $^{th}$)?

$3+6+9+12+\ldots+300 = \ldots$

With respect to the usual notations of an $A.P.$,if $T_{n} = 28$,$S_{n} = 144$,and $n = 9$,find the first term $a$.

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have $27$ flags to be fixed at intervals of every $2 \,m$. The flags are stored at the position of the middle-most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much total distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag? (in $m$)

The difference between two consecutive terms of an $A.P.$ is denoted by.........