A sequence is defined recursively by the given formulas Find

A sequence is defined recursively by the given formulas. Find the first five terms of the sequence. a_n = a_n - 1 + a_n - 2 + a_n - 3 and a_1 = a_2 = a_3 = 4 a_1 = a_2 = a_3 = a_4 = a_5 =

Solution

a₁= a₂=a₃ =4

a₄=a_4-1+a_4-2+a_4-3 = a₃+a₂+a₁ =4+4+4=12

a₅=a_5-1+a_5-2+a_5-3 =a₄+a₃+a₂ = 12+4+4=20