Question

this sequence represents the diameters of circles used to create an art project: 2.5 cm, 3.1 cm, 3.7 cm, 4.3 cm. let f(n) represent diameter in centimeters and n the term number in the sequence. which equation represents the sequence of diameters?
o f(n)=0.6n + 1.9
o f(n)=0.6n + 2.5
o f(n + 1)=f(n)+1.9
o f(n + 1)=f(n)-0.6

Explanation:

Step1: Check for arithmetic - sequence

Find the common difference between consecutive terms. $3.1 - 2.5=0.6$, $3.7 - 3.1 = 0.6$, $4.3 - 3.7=0.6$. It's an arithmetic sequence with common difference $d = 0.6$.

Step2: Recall the formula for arithmetic sequence

The general formula for an arithmetic sequence is $f(n)=f(1)+(n - 1)d$, where $f(1)$ is the first - term and $d$ is the common difference. Here $f(1)=2.5$ and $d = 0.6$.

Step3: Simplify the formula

$f(n)=2.5+(n - 1)\times0.6=2.5 + 0.6n-0.6=0.6n + 1.9$.

Answer:

A. $f(n)=0.6n + 1.9$