In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403. What is the first term?

Let a₁ be the first term....then the successive terms are

3a₁ + 4,  9a₁ + 16,  27a₁ + 52,  81a₁ + 160     

So .... 81a₁ + 160 = 403     subtract 160 from each side

81a₁ = 243    divide both sides by 81

a₁ = 3