Question

Use the recursive formula below to find the first four terms of the sequence. Use the Formula Editor x−−√ to type math or use the Image icon to upload a photo of your work.

a1=−5 and an=an−1(2)

Answer 1

To find the first four terms of the sequence defined by the recursive formula, we have:

1. The first term \( a_1 = -5 \).
2. The recursive relation \( a_n = a_{n-1} \times 2 \).

Now, we'll compute the subsequent terms step by step:

- **First term**:
\[
a_1 = -5
\]

- **Second term**: Using the recursive relation:
\[
a_2 = a_1 \times 2 = -5 \times 2 = -10
\]

- **Third term**: Again applying the recursive relation:
\[
a_3 = a_2 \times 2 = -10 \times 2 = -20
\]

- **Fourth term**: Continuing with the recursion:
\[
a_4 = a_3 \times 2 = -20 \times 2 = -40
\]

Thus, the first four terms of the sequence are:
\[
a_1 = -5, \quad a_2 = -10, \quad a_3 = -20, \quad a_4 = -40
\]