Question

Write the first five terms of the sequence defined by the recursive formula a subscript n baseline equals 5 a subscript n minus 1 baseline minus 1, with a subscript 1 baseline equals 0.
(1 point)
Responses

negative 1 comma negative 6 comma negative 31 comma negative 156 comma negative 781
Image with alt text: negative 1 comma negative 6 comma negative 31 comma negative 156 comma negative 781

0 comma negative 1 comma negative 6 comma negative 31 comma negative 156
Image with alt text: 0 comma negative 1 comma negative 6 comma negative 31 comma negative 156

4, 9, 14, 19, 24
4, 9, 14, 19, 24

negative 1 comma 4 comma 9 comma 14 comma 19
Image with alt text: negative 1 comma 4 comma 9 comma 14 comma 19

Answer 1

To find the first five terms of the sequence defined by the recursive formula \( a_n = 5a_{n-1} - 1 \) with \( a_1 = 0 \), we can compute each term step by step.

1. **For \( n = 1 \)**:
\[
a_1 = 0
\]

2. **For \( n = 2 \)**:
\[
a_2 = 5a_{1} - 1 = 5(0) - 1 = -1
\]

3. **For \( n = 3 \)**:
\[
a_3 = 5a_{2} - 1 = 5(-1) - 1 = -5 - 1 = -6
\]

4. **For \( n = 4 \)**:
\[
a_4 = 5a_{3} - 1 = 5(-6) - 1 = -30 - 1 = -31
\]

5. **For \( n = 5 \)**:
\[
a_5 = 5a_{4} - 1 = 5(-31) - 1 = -155 - 1 = -156
\]

So, the first five terms of the sequence are:

\[
0, -1, -6, -31, -156
\]

Based on the options provided, the correct response is:

**0, -1, -6, -31, -156**.