Question

Find the seventeenth term of the arithmetic sequence -4, -9, -15

Answer 1

When facing problems where you have to find a certain term of a sequence, look really closely for patterns. Some sequences have a really easy pattern like adding or subtracting numbers. Other sequences have more complicated patterns.

In this case, based solely on the three numbers you are given you can observe that the numbers are decreasing.

Here's what we can see so far:

To get from the 1st term to the 2nd term:
subtract 5 from the starting number
To get from the 2nd term to the 3rd term:
subtract 6 from the above result

Even though we only have a small piece of the pattern, let's try extending it! We're going to continue subtracting, but we're going to increase the amount that we take away every time.

Try solving it yourself before you look ahead! :)

So continuing the pattern:

Start at -4

To get from the 1st term to the 2nd term:
subtract 5
(-4 - 5) = -9

To get from the 2nd term to the 3rd term:
subtract 6
(-9 - 6) = -15

To get from the 3rd term to the 4th term:
subtract 7
(-15 - 7) = -22

To get from the 4th term to the 5th term:
subtract 8
(-22 - 8) = -30

To get from the 5th term to the 6th term:
subtract 9
(-30 - 9) = -39

[...continue this pattern until you reach the 17th term...]

Before you just write down the answer, make sure you do your own work! I calculated that the 17th term was -204.

Try practicing with some other sequences of numbers! You've got this!