Question

IRA HAS 120 SONGS ON HER PLAYLIST .EACH WEEK SHE DOWNLOIADS FOR NEW SONGS

Answer 1

• 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

Answer 2

`f(w)=116+4w`

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
`w` 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:
`a_n=a+(n-1)d`

where:

• 
  `a_n` 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
`a=120`

We are told that she adds 4 new songs each week, so
`d=4`

Also,
`n=w`

Substituting these values into the formula:

`\implies a_w=120+(w-1)4`

`\implies f(w)=116+4w`