Question

As your costumer increases, your list goes as follows, 12, 14, 16, 18,....

Questions:
1. If what you gain daily continues in this manner, how much gain can you
expect at the end of the week?

2. is your gain shows a pattern? If yes, find its general rule.

3. Using the general rule, compute for your expected gain at the end of 30
days.​

Answer 1

1. 24

2.
`10+2n` where n denotes number of days.

3. 70

Explanation:

1.

Consider the sequence:
`12,14,16,18,...`

Here,

`14-12=2\\16-14=2\\18-16=2`

Take the common difference as d = 2 and the first term as a = 12

Use the formula:
`a_n=a+(n-1)d`

To find expected gain at the end of the week, find
`a_7`

`a_7=12+(7-1)2\\=12+6(2)\\=12+12\\=24`

2.

Yes, the gain shows the pattern.

Put
`a=12,d=2` in
`a_n=a+(n-1)d`

`a_n=12+(n-1)2\\=12+2n-2\\=10+2n`

Here, n denotes number of days.

3.

To find expected gain at the end of 30 days, put
`n=30` in
`a_n=10+2n`

`a_(30)=10+2(30)\\ =10+60\\=70`