Final answer:
The terms a0, a1, a2, and a3 of the sequence an can be determined using the binomial theorem.
Step-by-step explanation:
The terms a0, a1, a2, and a3 of the sequence an can be determined using the given series expansions, particularly the binomial theorem. According to the binomial theorem, (a + b)^n = an + nan-1b + n(n-1)an-2b^2 + n(n-1)(n-2)an-3b^3 + ... + 2!an-2b^n-2 + anb^n. In this case, we can consider a as the constant term and b as the variable term. So, the terms a0, a1, a2, and a3 of the sequence are:
- a0 = a^0 = 1
- a1 = a^1 = a
- a2 = n(n-1)an-2b^2 = 2!ab^2 = 2ab^2
- a3 = n(n-1)(n-2)an-3b^3 = 3!ab^3 = 6ab^3