Final answer:
The sequence increases by 0.6 cm with each term, indicating a linear relationship. Using the formula f(n) = dn + c, where d is the common difference and c is the adjusted first term, we find the equation representing the sequence of diameters is f(n) = 0.6n + 1.9.
Step-by-step explanation:
The question asks for the equation that represents the sequence of diameters for a set of circles used in an art project. As the diameters increment by a constant difference (0.6 cm), this suggests a linear relationship between the term number n and the diameter f(n). If we observe the pattern, each term (starting from n = 1 onwards) is found by adding 0.6 to the previous term, with the first term being 2.5 cm.
To find the formula for the nth term, we can start with the first term, 2.5 cm, and add 0.6 cm for each subsequent term. To get this, we use the formula f(n) = dn + c, where d is the common difference between the terms and c is the first term reduced by the common difference (since term 1 would be c + d). Since our common difference d is 0.6 cm and our first term is 2.5 cm, c would be 2.5 cm - 0.6 cm = 1.9 cm. The equation representing the sequence of diameters is: f(n) = 0.6n + 1.9.