Grade 10 Maths · Number Patterns, Sequences and Series · Find a term in a repeating pattern

Find a term in a repeating pattern Grade 10

Use the length of the repeating cycle and the remainder after dividing to find any term, for example in A, B, C, A, B, C, … the 100th term is A because 100 3 leaves 1.

questions use it, all grades · 1 past paper, 14 practice: 15 questions use it, all grades · 1 past paper, 14 practice
videos: 2 videos

Learn it: find a term in a repeating pattern

Pick one and watch it, then try the questions below. Videos load only when you tap play.

How to find the term of a repeating sequence.MATHEMATICS PRO

Predicting a Term in a Repeating PatternSLA - The St. Lawrence Academy

Now try it on a question

No sign-up. Takes 3 minutes.

Question 3.2 · November 2024 · Paper 1 · Provincial · 3 marks

3.1 In each diagram below, there are shaded squares and white squares. Diagram for this question

3.2 If the pattern TERMSTERMS... continue on the same way, what will be the

38 3^{r d}

letter?(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More questions: find a term in a repeating pattern

Work each one out first, then open the memo and check every tick.

3. Practice · NavyBlue · 3 marks
Determine the units digit of $2^{50}$ without working out $2^{50}$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Cycle $2; 4; 8; 16; 32; \dots$
  Units digits: $2; 4; 8; 6; 2; \dots$ (cycle of $4$ )
  1 mark · Find a term in a repeating pattern
2. ✓
  Remainder $50 \div 4 = 12$ remainder $2$
  1 mark · Find a term in a repeating pattern
3. ✓
  Units digitSame as $2^{2}$ : units digit $4$
  1 mark · Find a term in a repeating pattern
4. Practice · Siyavula Grade 10 Maths · 3 marks
Use a calculator to explore the powers of $7$ and then generalise your findings to determine the tens digit of $7^{2008}$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Cycle $7^{1} = 07$ , $7^{2} = 49$ , $7^{3} = 343$ , $7^{4} = 2401$ , $7^{5} = 16807$
  Last two digits repeat: $07; 49; 43; 01; \dots$ (cycle of $4$ )
  1 mark · Find a term in a repeating pattern
2. ✓
  Remainder $2008 \div 4 = 502$ remainder $0$
  1 mark · Find a term in a repeating pattern
3. ✓
  Tens digitSame as $7^{4} = 2401$ : last two digits $01$
  The tens digit is $0$
  1 mark · Find a term in a repeating pattern
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
5. Practice · NavyBlue · 2 marks
Thandi threads beads onto a string in the repeating order red, red, blue, green, yellow, red, red, blue, green, yellow, ...
How many of the first $100$ beads are red?(2)
Show the memo (2 ticks)Memo
1. ✓
  Full cycles $100 \div 5 = 20$ full cycles, remainder $0$
  1 mark · Find a term in a repeating pattern
2. ✓
  Red beads $20 \times 2 = 40$ red beads
  1 mark · Find a term in a repeating pattern
6. Practice · Siyavula Grade 10 Maths · 3 marks
What is the $34 6^{th}$ letter of the sequence COMMONCOMMON...?(3)
Show the memo (3 ticks)Memo
1. ✓
  Cycle lengthThe word repeats every $6$ letters.
  1 mark · Find a term in a repeating pattern
2. ✓
  Divide $346 \div 6 = 57$ remainder $4$
  1 mark · Find a term in a repeating pattern
3. ✓
  LetterThe letter is M.
  1 mark · Find a term in a repeating pattern
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills