Question

17, 13, 9,5...
determine the sequence

Answer 1

When determining sequences, it's easiest to take a look at two individual items in the sequence, separate them from the group, and determine how to get from the first to the next. You then do this with each subsequent pair until you determine the pattern.

First, look at 17 and 13. How do we get from 17 to 13? The easiest answer is subtraction: 17 - 4 = 13. Let's leave that there and move on to the next pair.

Next, 13 to 9. Let's try subtraction again like we did before. 13 - 4 = 9. Just like in the first pair, subtracting by 4 got us to the next number. Let's see if that works in the next pair.

Finally, 9 to 5. 9 - 4 = 5. Subtracting by 4 worked for this one too!

Therefore, the sequence is each number is subtracted by 4. The next number would be the difference of 5 - 4.

Answer 2

This is an arithmetic sequence because we are adding the same amount each time. In this case, we are adding -4 to each term to get the next term

17 + (-4) = 13

13 + (-4) = 9

9 + (-4) = 5

and so on. The starting term is
`a_1 = 17`

The common difference is
`d = -4`

The nth term of the arithmetic sequence can be found by this formula

`a_n = a_1 + d(n-1)\\\\a_n = 17 + (-4)(n-1)\\\\a_n = 17 - 4n + 4\\\\a_n = -4n+21`

For instance, if n = 2, then,

`a_n = -4n+21\\\\a_2 = -4(2)+21\\\\a_2 = -8+21\\\\a_2 = 13`

which matches up with the second term listed.