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.

Question

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: \[ a_1 = -5, \quad a_2 = -10, \quad a_3 = -20, \quad a_4 = -40 \]