Write the first five terms of the sequence defined by the recursive formula a subscript n baseline equals 2 times left-parenthesis a subscript n minus 1 baseline right-parenthesis plus 5, with a subscript 1 baseline equals negative 3.

Question

(1 point)
Responses

negative 3 comma negative 10 comma negative 24 comma negative 43 comma negative 81
Image with alt text: negative 3 comma negative 10 comma negative 24 comma negative 43 comma negative 81

negative 3 comma negative 1 comma 3 comma 11 comma 27
Image with alt text: negative 3 comma negative 1 comma 3 comma 11 comma 27

negative 3 comma 2 comma 7 comma 12 comma 17
Image with alt text: negative 3 comma 2 comma 7 comma 12 comma 17

negative 3 comma 4 comma 18 comma 46 comma 102

Answer 1

To find the first five terms of the sequence defined by the recursive formula \( a_n = 2(a_{n-1}) + 5 \) with the initial value \( a_1 = -3 \), we will calculate each term step-by-step.

1. First Term: \( a_1 = -3 \)

2. Second Term: \[ a_2 = 2(a_1) + 5 = 2(-3) + 5 = -6 + 5 = -1 \]

3. Third Term: \[ a_3 = 2(a_2) + 5 = 2(-1) + 5 = -2 + 5 = 3 \]

4. Fourth Term: \[ a_4 = 2(a_3) + 5 = 2(3) + 5 = 6 + 5 = 11 \]

5. Fifth Term: \[ a_5 = 2(a_4) + 5 = 2(11) + 5 = 22 + 5 = 27 \]

Putting it all together, the first five terms of the sequence are: \[ -3, -1, 3, 11, 27 \]

Therefore, the correct response is: negative 3, negative 1, 3, 11, 27.