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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?

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ANSWER

The expression that represent the sequence of diameters is,
[tex]f(n) = 0.6n + 1.9[/tex]


EXPLANATION

The terms in the sequence are,

[tex]2.5,3.1,3.7,4.3[/tex]


The first term is
[tex]a = 2.5[/tex]

The common difference is

[tex]d = 3.1 - 2.5 = 0.6[/tex]


The formula for the nth term is given by,


[tex]f(n) = a + (n - 1)d[/tex]



We substitute the values in to the formula to get,



[tex]f(n) = 2.5+ (n - 1)0.6[/tex]



We expand the parenthesis to obtain,

[tex]f(n) = 2.5 + 0.6n - 0.6[/tex]



We rearrange to obtain,

[tex]f(n) = 0.6n + 2.5- 0.6[/tex]


We simplify to get,

[tex]f(n) = 0.6n + 1.9[/tex]

Answer:

[tex]f(n) = 1.9 +0.6n[/tex]

Step-by-step explanation:

The nth term of the arithmetic sequence is given by:

[tex]a_n = a_1+(n-1)d[/tex]            ....[1]

where

[tex]a_1[/tex] is the first term

d is the common difference and n is the number of terms.

Here, f(n) represent diameter in centimeters and n the term number in the sequence.

Given the sequence represents the diameters of circles used to create an art project:

2.5 cm, 3.1 cm, 3.7 cm , 4.3 cm

This sequence is an arithmetic sequence with

[tex]a_1[/tex] = 2.5 and d = 0.6

Since,

3.1-2.5 = 0.6,

3.7-3.1 = 0.6

4.3-3.7 = 0.6

Substitute the given values in [1] we have;

[tex]f(n) =2.5+(n-1)(0.6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a \cdot b+ a\cdot c[/tex]we have;

[tex]f(n) = 2.5+0.6n-0.6[/tex]

Simplify:

[tex]f(n) = 1.9 +0.6n[/tex]

Therefore, the equation represents the sequence of diameters is, [tex]f(n) = 1.9 +0.6n[/tex]

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