Question

a sequence is defined recursively by the formula $f(n + 1) = f(n) + 3$. the first term of the sequence is $-4$. what is the next term in the sequence?
$\circ$ $-7$
$\circ$ $-1$
$\circ$ $1$
$\circ$ $7$

Explanation:

Step1: Identify the first term and the recursive formula

The first term \( f(1) = -4 \), and the recursive formula is \( f(n + 1)=f(n)+3 \). To find the next term (when \( n = 1 \)), we need to calculate \( f(2) \).

Step2: Apply the recursive formula

Substitute \( n = 1 \) into the formula \( f(n + 1)=f(n)+3 \). So \( f(2)=f(1)+3 \). We know \( f(1)= - 4 \), then \( f(2)=-4 + 3 \).

Step3: Calculate the result

\( -4+3=-1 \).

Answer:

\(-1\) (corresponding to the option: \(-1\))