Nth term GCSE lesson: linear sequences as dots on a line, and is it a term?

Sequences and the nth term: practice

Show your working on paper. Check each nth term with n = 1 and n = 2. Write negative numbers with a minus sign. The stretch is optional.

Diagnostic question: choose and explain

1. What is the nth term of 4, 9, 14, 19, …?
   1. n + 5
   2. 5n + 4
   3. 5n − 1
   4. 5n

Practice questions

1. The nth term of a sequence is 4n + 3. What is the 10th term?
2. The first three terms of 2n + 5 are ___, ___ and ___
3. 3, 10, 17, 24, … has the nth term ___n − ___
4. 30, 26, 22, 18, … has the nth term ___ − ___n
5. Is 75 a term of the sequence 4, 7, 10, 13, …?
   1. Yes
   2. No
6. Which term of 6, 11, 16, 21, … is 96? (Give its position, n.)
7. The terms of a sequence are plotted as points (n, term). They lie on the line y = 4x − 3. What is the sequence?
   1. 4, 8, 12, 16, …
   2. 1, 5, 9, 13, …
   3. −3, 1, 5, 9, …
   4. −3, −7, −11, −15, …
8. One sequence has nth term 4n + 1, another 50 − 3n. They have the same term at position n = ___, where both are ___
9. The nth term is 3n + 2. Is the 20th term double the 10th term?
   1. Yes: 20 is double 10
   2. No: the 20th is 62, the 10th is 32
10. Stretch: 2, 5, 10, 17, 26, … goes up 3, 5, 7, 9, so it is not linear. Compare it with n²: its nth term is n² + ___, and its 10th term is ___

Support: For question 3: the terms go up 7 each time, so start from 7n: 7, 14, 21, 28. How far is each term from that? For question 5: write the nth term first, then make it equal to the number and solve. A term needs a whole number n.

Sequences and the nth term: exit

Show your working; one sentence for the second part.

1. The nth term of a sequence is 6n − 4. Is 100 a term? Show how you know. Then say in one sentence what the 6 means on a graph of the terms as points (n, term).

Exit check

One test of a number and one sentence about the graph show who has the whole idea.

Students solve 6n − 4 = 100 and decide.

Sequences and the nth term: rules and terms

Show your working. Check every nth term with n = 1 and n = 2. Question 6 is for Higher.