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?
( \bigcirc f(n)=0.6n + 1.9 )
( \bigcirc f(n)=0.6n + 2.5 )
( \bigcirc f(n + 1)=f(n)+1.9 )
( \bigcirc f(n + 1)=f(n)-0.6 )

Explanation:

Step1: Check if it is an arithmetic sequence

Find the common difference \(d\). \(d = 3.1−2.5=0.6\), \(d = 3.7 - 3.1=0.6\), \(d=4.3 - 3.7 = 0.6\). So it is an arithmetic sequence with \(a_1=2.5\) and \(d = 0.6\).
The formula for the \(n\)th term of an arithmetic sequence is \(f(n)=a_1+(n - 1)d\).

Step2: Substitute \(a_1\) and \(d\) into the formula

Substitute \(a_1 = 2.5\) and \(d=0.6\) into \(f(n)=a_1+(n - 1)d\).

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Check the recursive formula: \(f(n + 1)=f(n)+d\), since \(d = 0.6\), \(f(n + 1)=f(n)+0.6\), so the third and fourth options are wrong. For the second option, when \(n = 1\), \(f(1)=0.6\times1+2.5=3.1
eq2.5\)

Answer:

\(f(n)=0.6n + 1.9\) (the first option)