Question

Complete the following by filling in the missing terms in the sequence

Answer 1

Let's begin with the first sequence:

`?,2,6,18,54,\text{?}`

We can see each term of the sequence after the 2 is the previous term multiplied by 3. So the missing terms would be 2/3 and 54*3:

`(2)/(3),2,6,18,54,162.`

For the second sequence, we have:

`?,?,17,12,7,2.`

We can see that after the 17, each term is the previous one minus 5. So the sequence is:

`27,22,17,12,7,2.`

The third and fourth sequences are written correctly in the image.

For the fifth sequence, the only information we have to determine the ruele it's following is that the next number after 9 is 16, and the 1 that is before the number before the 9.

One possible rule would be to consider the sequence

`x_n=n^2\text{.}`

This way, if we start from n=0 we get:

`0,1,4,9,16,25,`

which fits the numbers we were given perfectly.