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

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

∴ 2nd option i.e.  is the correct option.

Step-by-step 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  

where:

= nth term

= first term

= term position

= common difference

In our case, the Arithmetic sequence is

12, 22, 32, 42,...

computing the differences of all the adjacent terms

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

Important Tip:

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

Now using the nth term formula of the Arithmetic sequence

now substituting and in the formula

simplifying

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

∴ 2nd option i.e.  is the correct option.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

step-by-step explanation: