#### Answer

$$\sum_{k=1}^{7} (-1)^{k+1}k^2$$

#### Work Step by Step

The sequence involves a sum with alternating signs (positive, then negative, then positive, and so on...).
This means that the summation involves either $(-1)^k$ or $(-1)^{k+1}$.
The first term is positive so it $-1)^{k+1}$ will be used.
Each term of the sequence involves a square of counting number, starting at $1$.
This means that the summation involves $k^2$.
The summation has 7 terms so $k$ is from 1 to 7 only.
Thus, the summation notation whose expanded form is given is:
$$\sum_{k=1}^{7} (-1)^{k+1}k^2$$