write the first five terms of the sequence defined by the recursive formula an = 2 (an-1)+5, with a1 = -3
To find the first five terms of the sequence defined by the recursive formula aₙ = 2(aₙ₋₁) + 5, with a₁ = -3, we can use the formula repeatedly.
First term:
a₁ = -3
Second term:
a₂ = 2(a₁) + 5 = 2(-3) + 5 = -6 + 5 = -1
Third term:
a₃ = 2(a₂) + 5 = 2(-1) + 5 = -2 + 5 = 3
Fourth term:
a₄ = 2(a₃) + 5 = 2(3) + 5 = 6 + 5 = 11
Fifth term:
a₅ = 2(a₄) + 5 = 2(11) + 5 = 22 + 5 = 27
Therefore, the first five terms of the sequence are: -3, -1, 3, 11, 27.