A sequence is defined recursively by a1=1,an=(an-1+1)^2. Write the first 4 terms of the sequence.

a1=1

a2=(a2-1+1)^2
=(a1+1)^2
=(1+1)^2
=4
a3=(a2+1)^2=5^2=25
a4=(a3+1)^2=(25+1)^2=26^2=676

Thank you!!!!! I see my mistake now...

You're welcome!

To find the first four terms of the sequence defined recursively by a1=1 and an=(an-1+1)^2, we can apply the recurrence relation repeatedly.

Term 1: Given a1=1, the first term of the sequence is 1.

Term 2: Now, we can use the recurrence relation to find the second term.
Substituting n=2 into the recurrence relation, we have:
a2 = (a2-1 + 1)^2 = (a1 + 1)^2 = (1 + 1)^2 = 2^2 = 4.
So, the second term of the sequence is 4.

Term 3: Applying the recurrence relation again, we can find the third term:
a3 = (a3-1 + 1)^2 = (a2 + 1)^2 = (4 + 1)^2 = 5^2 = 25.
Hence, the third term of the sequence is 25.

Term 4: Finally, we can calculate the fourth term using the recursion:
a4 = (a4-1 + 1)^2 = (a3 + 1)^2 = (25 + 1)^2 = 26^2 = 676.
Therefore, the fourth term of the sequence is 676.

In summary, the first four terms of the sequence are: 1, 4, 25, 676.