the first five terms of the sequence defined by the recursive formula a n =2*(a n-1 )+5 with a_{1} = - 3
To find the first five terms of the given recursive sequence, we can substitute the previous terms into the formula.
Using the given recursive formula, we have:
a₁ = -3
Now, we can find a₂:
a₂ = 2*(a₁) + 5
a₂ = 2*(-3) + 5
a₂ = -6 + 5
a₂ = -1
Next, we can find a₃:
a₃ = 2*(a₂) + 5
a₃ = 2*(-1) + 5
a₃ = -2 + 5
a₃ = 3
Continuing this process, we can find a₄ and a₅:
a₄ = 2*(a₃) + 5
a₄ = 2*(3) + 5
a₄ = 6 + 5
a₄ = 11
a₅ = 2*(a₄) + 5
a₅ = 2*(11) + 5
a₅ = 22 + 5
a₅ = 27
Therefore, the first five terms of the sequence are:
a₁ = -3
a₂ = -1
a₃ = 3
a₄ = 11
a₅ = 27