Two facts fix the list
A list adds the same step each time. Its 4th term is 14. Its 9th term is 34. What is the list?
a + 3d = 14. Step 1 of 4
- The 4th term is 14. So
a + 3d = 14. - The 9th term is 34. So
a + 8d = 34. - Subtract the first from the second.
5d = 20, sod = 4. - Put d back:
a = 14 − 12 = 2. The list is 2, 6, 10, 14, …
The rule
The list is 2, 6, 10, 14, and so on. Here a is the first term. The step is d.
Write each fact as a + (n − 1)d. Subtract to get d. Then find a.
The two equations have the same a. Subtracting makes a cancel. That leaves d alone.
Check the list. The 9th term is 2 + 8 × 4 = 34. The 4th term is 2 + 3 × 4 = 14. Both facts hold.
| Question | Working | Answer |
|---|---|---|
| What is the 20th term? | 2 + 19 × 4 | 78 |
| Which term is 90? | 2 + 4(n − 1) = 90 | 23rd |
| Is 51 a term? | 2 + 4(n − 1) = 51 | No, n = 13.25 |
Sometimes one fact gives d alone. Suppose the 14th term is 15 more than the 11th. Then 3d = 15, so d = 5. The 14th term is 3 steps after the 11th. That is why the gap of 15 is 3d.
Now try it. Slide a and d until both terms match.
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