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