Question

1. which function represents the following sequence? 42, 48, 54, 60 a. f(n) = 6n + 42 b. f(n) = 6n + 36 c. f(n) = 42n + 6 d. f(n) = 36n + 6

Explanation:

Step1: Identify sequence type

This is an arithmetic sequence with common difference $d = 48 - 42 = 6$.

Step2: Match to linear function

For $n=1$, $f(1)=42$. Test option B: $f(1)=6(1)+36=42$. For $n=2$, $f(2)=6(2)+36=48$, which matches.

Step3: Verify all terms

$n=3$: $6(3)+36=54$, $n=4$: $6(4)+36=60$. All terms match.

Answer:

B. $f(n)=6n + 36$