Question

a sequence is defined recursively by the formula $f(n + 1) = -2f(n)$. the first term of the sequence is $-1.5$. what is the next term in the sequence?
0.5
3
-3.5
-3

Explanation:

Step1: Identify the first term

The first term \( f(1) = -1.5 \).

Step2: Apply the recursive formula

The recursive formula is \( f(n + 1) = -2f(n) \). To find the next term (when \( n = 1 \), we find \( f(2) \)), substitute \( n = 1 \) into the formula:
\( f(2) = -2 \times f(1) \)
Substitute \( f(1) = -1.5 \) into the equation:
\( f(2) = -2 \times (-1.5) \)

Step3: Calculate the value

\( -2 \times (-1.5) = 3 \)

Answer:

3 (corresponding to the option "3")