Page 22 - MAT KS3 Y8 Cambridge CheckPoint

2.1 Generating sequences

3 This is part of Zalika’s homework.
a Is Zalika’s answer correct? Question The first term of a sequence is 3.
b Explain how her method works. The term-to-term rule is ‘add 12’.
c The first term of a sequence is 5. Work out the 10th term of the
The term-to-term rule is ‘add 8’. sequence.
Use Zalika’s method to work out: Answer 10 – 1 = 9, 9 × 12 = 108
i the 10th term ii the 20th term 3 + 108 = 111 10th term = 111
rm
iii the 50th term of the sequence.

4 Ahmad is trying to solve this problem. The fourth term of a sequence is 39.
Work out the answer to the problem. The term-to-term rule is ‘add 7’.
Explain how you solved the problem.
Work out the first term of the sequence.

5 Mia is trying to solve this problem. The 12th term of a sequence is 16.
Work out the answer to the problem. The term-to-term rule is ‘subtract 3’.
Explain how you solved the problem.
Work out the third term of the sequence.

6 The table shows two of the terms in a sequence.
Position-to-term rule: term = position number + 7 Position number 1 2 3 4 5 10 20
Copy the table. Use the position-to-term rule
to work out the missing numbers. Term 9 17
7 Use the position-to-term rule to work out the first four terms of each sequence.
a term = 6 × position number b term = position number – 4
c term = 2 × position number + 1 d term = 3 × position number – 1
8 Use the position-to-term rules to work out:
i the 10th term ii the 20th term iii the 100th term of each sequence.
a term = position number + 5 b term = 2 × position number
c term = 4 × position number + 8 d term = 5 × position number – 25

9 The fourth term of a sequence is 11. The seventh term of the sequence is 20.
Which of these position-to-term rules is the correct one for the sequence?
A term = position number + 7 B term = 2 × position number + 3
C term = 3 × position number − 1 D term = 4 × position number − 5
Show how you worked out your answer.
10 This is part of Razi’s homework.

Question The position-to-term rule of a sequence is:
term = 3 × position number + 2
Work out the first three terms of the sequence.
Answer 1st term = 3 × 1 + 2 = 5 2nd term = 3 × 5 + 2 = 17
3rd term = 3 × 17 + 2 = 53

Is Razi’s homework correct? Explain your answer.
20 2 Sequences, expressions and formulae