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?\
\bigcirc $-3.5$\
\bigcirc $-3$\
\bigcirc $0.5$\
\bigcirc $3$

Explanation:

Step1: Identify the first term

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

Step2: Apply the recursive formula

We need to find the next term, which is \( f(2) \). Using the formula \( f(n + 1) = -2f(n) \), when \( n = 1 \), we have \( f(2) = -2 \times f(1) \).
Substitute \( f(1) = -1.5 \) into the formula: \( f(2) = -2 \times (-1.5) \).
Calculate the product: \( -2 \times (-1.5) = 3 \).

Answer:

3