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

How many terms of the $AP: -15, -13, -11, \ldots$ are needed to make the sum $-55$? Explain the reason for the double answer.

Four numbers in increasing order form an $A.P.$ The sum of those numbers is $32$ and the ratio of the product of extremes to the product of means is $7: 15$. Find those numbers.

Find the value of the middle most term$(s)$ of the $AP:$ $-11, -7, -3, \ldots, 49$.

The sum of how many terms of the $A.P.$ $54, 51, 48, \dots$ is $513$? Explain the reason for getting two different answers.

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 7 - 3n$. Find the sum of the first $25$ terms of the $A.P.$