Lesson 9 of 14
Is it a term of the list?
Show on a big screenThe list 4, 9, 14, 19, … has no last term. Is 104 in it?
Step 1 of 4
- The list starts at a = 4. Each step is d = 5.
- Is 104 a term? Put it in the rule:
4 + 5(n − 1) = 104. 5(n − 1) = 100, son − 1 = 20andn = 21.- 21 is whole. So 104 is the 21st term. For 105,
n = 21.2. That is not a term.
The rule
Yes. 104 is the 21st term of the list. This test is for a list with the same step each time. Here a is the first term and d is the step.
Put the number in aₙ = a + (n − 1)d. A term needs n to be a whole number, at least 1.
The letter n counts places: 1st, 2nd, 3rd. So it cannot be a fraction. It cannot be 0 or negative.
| Question | Put in | n | Answer |
|---|---|---|---|
| Is 104 a term of 4, 9, 14, …? | 4 + 5(n − 1) = 104 | 21 | Yes, the 21st |
| Is 105 a term of 4, 9, 14, …? | 4 + 5(n − 1) = 105 | 21.2 | No |
| Which term of 40, 37, 34, … is −50? | 40 − 3(n − 1) = −50 | 31 | The 31st |
| How many terms in 2, 9, 16, …, 100? | 2 + 7(n − 1) = 100 | 15 | 15 terms |
The last row counts terms. The last term is 100, so n is the number of terms.
For 40, 37, 34, …, a = 40 and d = −3. Then 3(n − 1) = 90, so n = 31. For 2, 9, 16, …, a = 2 and d = 7. Then 7(n − 1) = 98, so n = 15.
Now try it. Read the list. Tap the answer.
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