Use the value of the acceleration due to the gravity $g=9.8~{\rm m/s}^2$.
If the Slinky spring is suspended by one end, the extension of its turns in the upper and lower parts will differ. Number the spring coils from top to bottom and denote the coil number by $n$. Let $L_n$ denote the distance between the beginning of the $n$-th turn and the end of the $(n+1)$-th turn (i.e., the length of two turns — the $n$-th one and the next one).
Let us proceed to the theoretical description of the Slinky. Let $m_0$ be the mass of a single turn, and $k$ be the stiffness coefficient of a single turn. As before, we will number the spring turns from top to bottom. Let $l_n$ denote the distance between the beginning and the end of the $n$-th turn.
Consider the system of bodies consisting of the $n$-th turn and all the others located below it.
Note that in the undeformed state, the spring turns are pressed tightly against each other. Therefore, the deformation $\Delta l_n$ of the turn, which appears in the expression for the elastic force $F_{\text{el}}=k\Delta l_n$, will be considered equal to its length $l_n$ (i.e. $F_{\text{el}}=kl_n$).
In question A3, measurements were taken of the length $L_n$ of two turns — the $n$-th and the $(n+1)$-th. Therefore, $L_n=l_n + l_{n+1}$.
If you place the Slinky spring on a scale and vertically lift its upper end to a height $H$, the scale readings will decrease.
First, turn on the scale, then place the Slinky spring on it. Secure the top turn of the spring in the stand clamp. By adjusting the position of the stand clamp, one can change the value of $H$.
Let us investigate the dependence of $m$ on $H$ theoretically. As in the first part of the problem, let us number the turns from top to bottom. Again let $l_n$ denote the deformation of the $n$-th turn. Note that during each of the experiments, only a part of the spring's turns, located at the top, is deformed. Let $X$ be the number of spring turns that are deformed. The remaining $N-X$ turns simply lie on the scale.
In this case, the extension of the entire spring (which is the value $H$) can be determined as:
$$H=\sum_{n=1}^X l_n.$$
Mathematical Hint. A number sequence of the form $a$, $a+d$, $\ldots$, $a+(n-1)d$, $\ldots$ is called an arithmetic progression. Each number in such a sequence, starting from the second, is obtained from the previous one by adding a constant number. The general form of the $n$-th term of the sequence is $a_n=a_1+(n-1)d$.
The following formula holds for the sum $S_X$ of the first $X$ terms of an arithmetic progression:
$$S_X=\sum_{n=1}^X a_n=\frac{a_1+a_X}{2}\cdot X.$$
Consider the $N-X$ turns lying on the scale as a system of bodies.
Hint. When solving the next question, you may assume that the number of deformed turns is $X \gg 1$. In this case, in particular, $X(X+1)\simeq X^2$.