Question

For number 5 why was that the answer? can someone please help to explain number 5.

Answer 1

The explicit rule for the sequence in the table above is:

`f_n=10n+2`

∴ 2nd option i.e.
`f_n=10n+2` is the correct option.

Explanation:

Given the table

Tickets 1 2 3 4

Total Cost 12 22 32 42

An arithmetic sequence has a constant difference 'd' and is defined by

`f_n=f_1+\left(n-1\right)d`

where:

`f_n` = nth term

`f_1` = first term

`n` = term position

`d` = common difference

In our case, the Arithmetic sequence is

12, 22, 32, 42,...

computing the differences of all the adjacent terms

`22 - 12 = 10, 32 - 22 = 10, 42 - 32 = 10`

The difference between all the adjacent terms is the same and equal to

`d = 10`

Important Tip:

As the first term involves the cost of 1 ticket which is 12, thus

`f_1=12`

Now using the nth term formula of the Arithmetic sequence

`f_n=f_1+\left(n-1\right)d`

now substituting
`f_1=12` and
`d = 10` in the formula

`\:fn=10\left(n-1\right)+12`

`f_n=10n-10+12\:`

simplifying

`f_n=10n+2`

Therefore, the explicit rule for the sequence in the table above is:

`f_n=10n+2`

∴ 2nd option i.e.
`f_n=10n+2` is the correct option.