General rule for arithmetic sequence: 4,11,18,25,32,39

First, lets find out how much each number goes up by in the sequence:

Lets subtract 4 from 11:

11 - 4 = 7

Lets do it again with another pair of numbers to make sure all of the numbers go up by 7:

18 - 11 = 7

Now we know that the sequence goes up by 7 each time.

Next, lets compare the sequence to the 7 times table: (since sequence goes in 7's)

7    14    21    28    35    42             (7 times table)

4   11     18    25    32    39             (Sequence)

Lets see the difference between the 7 times table and the sequence.

We do this by subtracting on number from the sequence from the opposite number from the 7 times table.

Lets choose 7 and 4:

7 - 4 = 3              So the difference between the sequence and the 7 times                    table is 3

This means that we get the sequence by using the 7 times table minus 3:  (7times table - 1)

Therefore the General Rule for the arithmetic sequence is:

7n - 3            

(note:   n stands for the term for a sequence. For example, 11 is the 2nd term in the sequence)

7n - 3      

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: