Question

given the recursive rule, find the 4th term of the sequence. f(1) = 6, f(n) = f(n - 1) - 1.5. options: 1.5, 10.5, -1, -2

Explanation:

Step1: Find the 2nd term

We know that \( f(1) = 6 \) and the recursive formula is \( f(n)=f(n - 1)-1.5 \). For \( n = 2 \), we substitute \( n-1=1 \) into the formula. So \( f(2)=f(1)-1.5 \). Substituting \( f(1) = 6 \), we get \( f(2)=6 - 1.5=4.5 \).

Step2: Find the 3rd term

For \( n = 3 \), we use the recursive formula \( f(3)=f(2)-1.5 \). We already found that \( f(2) = 4.5 \), so \( f(3)=4.5-1.5 = 3 \).

Step3: Find the 4th term

For \( n=4 \), we use the recursive formula \( f(4)=f(3)-1.5 \). We found that \( f(3)=3 \), so \( f(4)=3 - 1.5=1.5 \).

Answer:

1.5 (corresponding to the first option among the given choices)