Several terms of a sequence $\left\{a_{n}\right\}_{n=1}^{\infty}$ are given below.
\[
\{1,-5,25,-125,625, \ldots\}
\]
a. Find the next two terms of the sequence.
b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence)
c. Find an explicit formula for the general nth term of the sequence.
a. The next two terms of the sequence are $a_{6}=\square$ and $a_{7}=\square$. (Simplify your answers.)

Step 1 ：The given sequence is \(\{1,-5,25,-125,625, \ldots\}\).

Step 2 ：This appears to be a geometric sequence, where each term is multiplied by -5 to get the next term.

Step 3 ：We can confirm this by dividing each term by the previous term, which should give a constant ratio if the sequence is indeed geometric.

Step 4 ：The sequence is indeed geometric with a ratio of -5.

Step 5 ：Using this ratio, we can find the next two terms of the sequence by multiplying the last given term by -5 for each subsequent term.

Step 6 ：The next term after 625 is \(625 \times -5 = -3125\).

Step 7 ：The term after -3125 is \(-3125 \times -5 = 15625\).

Step 8 ：\(\boxed{\text{The next two terms of the sequence are } a_{6}=-3125 \text{ and } a_{7}=15625}\)