Final answer:
The first term of the sequence is √401 and the second term is 1604.
Step-by-step explanation:
The given sequence is defined recursively by the formula aⁿ=(aⁿ-1)² 4. The initial condition is a⁴=1604. We need to find the first two terms of the sequence.
Using the formula, we can substitute the given initial condition into it:
a⁴ = (a⁴-1)² 4
1604 = (a³)² 4
Dividing both sides of the equation by 4, we get:
401 = (a³)²
Taking the square root of both sides of the equation:
√401 = a³
Therefore, the first term of the sequence is √401.
To find the second term, we substitute a³ (the first term) into the formula:
a⁴ = (√401)² 4
Simplifying the equation:
a⁴ = 401 4
a⁴ = 1604
Thus, the second term of the sequence is 1604.