Number Patterns

6 Grade 7 Mathematics questions on Number Patterns, with worked marking schemes. 6 questions are available on this topic in full.

1. Question 1

   1 mark

   Find the next term: 3, 6, 11, 18, 27, ___

   A. 35

   B. 36

   C. 40

   D. 38

   (1 mark)

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2. Question 2

   3 marks

   The first term of an arithmetic sequence is 4 and the common difference is 7. Find the sum of the first 10 terms.

   (3 marks)

   Marking scheme

   In an arithmetic sequence the $n$th term is $a+(n-1)d$. With $a=4$ and $d=7$, the $10$th term is $4+9\times 7=67$. (1)

   The sum of $n$ terms is $S_n=\frac{n}{2}(a+l)$, where $l$ is the last term. (1)

   $S_{10}=\frac{10}{2}(4+67)=5\times 71=355$. (1)

   Final answer: $355$.

3. Question 3

   3 marks

   Find the rule and the 15th term for: 2, 5, 10, 17, 26, ...

   (3 marks)

   Marking scheme

   Look at the gaps: $3$, $5$, $7$, $9$ — they grow by $2$ each time, which happens when the rule involves $n^2$. (1)

   Compare with the square numbers $1,4,9,16,25$: each term is exactly one more, so the rule is $n^2+1$. (1)

   For the $15$th term put $n=15$: $15^2+1=225+1=226$. (1)

   Final answer: the rule is $n^2+1$ and the $15$th term is $226$.

4. Question 4

   1 mark

   The sequence 2, 6, 18, 54, ... is a:

   A. Geometric sequence

   B. Fibonacci sequence

   C. Square number sequence

   D. Arithmetic sequence

   (1 mark)

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5. Question 5

   1 mark

   What is the nth term for: 5, 8, 11, 14, ...?

   A. 5n

   B. n + 3

   C. 3n + 2

   D. 3n − 1

   (1 mark)

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6. Question 6

   1 mark

   Find the 20th term of the sequence: 7, 12, 17, 22, ...

   A. 100

   B. 107

   C. 97

   D. 102

   (1 mark)

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