Respuesta :

  • She has initially 120songs

If she adds songs new in constant amount like 2 per week

Then it will form an arithmetic sequence.

  • Where common difference is d

semsee45

Answer:

[tex]f(w)=116+4w[/tex]

Step-by-step explanation:

Question

Iris has 120 songs on her playlist.  Each week, she downloads 4 new songs.  Write an expression to show the total number of songs on Iris's playlist after [tex]w[/tex] weeks.

Solution

This scenario can be modeled as an arithmetic sequence since Iris is adding a constant number of songs to her playlist each week.

Arithmetic sequence

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

  • [tex]a_n[/tex] is the nth term
  • a is the first term
  • d is the common difference between terms

We are told that she starts with 120 songs on her playlist, so [tex]a=120[/tex]

We are told that she adds 4 new songs each week, so [tex]d=4[/tex]

Also, [tex]n=w[/tex]

Substituting these values into the formula:

[tex]\implies a_w=120+(w-1)4[/tex]

[tex]\implies f(w)=116+4w[/tex]

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