Grade 11 Maths · Number Patterns, Sequences and Series

Use a pattern's first differences

Treat the gaps between terms of a quadratic pattern as their own pattern, for example find which two terms differ by 25.

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number pattern... between which two consecutive terms is the first difference....Kasi Maths - (Mr Sjumba)

between which two terms of the quadratic sequence will the difference be -121. sequence and seriesBenit mathematics

Quadratic Pattern Grade 11 ExamKevinmathscience

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Question 3.2 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

Given the quadratic sequence:

14; 9; 6; 5; ...

3.2 Two consecutive terms of the quadratic sequence have a difference of

33

. Calculate the value of the larger term.(3)

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

More past paper questions: use a pattern's first differences

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3. Question 2.2.1 · November 2024 · Paper 1 · National (DBE) · 3 marks
2.2 The sequence of the first differences of a quadratic pattern is: $1; 3; 5; ...$
2.2.1 If $T_{99}$ of this quadratic pattern is $9632$ , calculate the value of $T_{98}$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Calculate the 98th first differenceFirst differences form arithmetic sequence: $T_{n} = 2 n - 1$
  $9 8^{t h}$ difference $= 2 (98) - 1 = 195$
  1 mark · Use a pattern's first differences
2. ✓
  Subtract difference from T99 $T_{99} - T_{98} = 1^{s t} difference_{98}$
  $T_{98} = 9632 - 195$
  1 mark · Use a pattern's first differences
3. ✓
  Final Answer $T_{98} = 9437$
  1 mark · Use a pattern's first differences
4. Question 3.1.2 · May/June 2024 · Paper 1 · National (DBE) · 4 marks
3.1 Consider the quadratic number pattern: $3; 7; 12; \dots$
3.1.2 What number must be added to $T_{n - 1}$ so that $T_{n} = 13527$ ?(4)
Show the memo (4 ticks)Memo
1. ✓
  Equate general term to target value $13527 = 0, 5 n^{2} + 2, 5 n$
  1 mark · Use a quadratic general term
2. ✓
  Solve quadratic equation for n $n = 162$
  1 mark · Use the quadratic formula
3. ✓
  Determine value of n-1 term $T_{161} = 13363$
  1 mark · Use a quadratic general term
4. ✓
  Calculate difference $13527 - 13363 = 164$
  1 mark · Use a pattern's first differences
5. Question 3.1.5 · March 2018 · Provincial · 2 marks
3.1 Consider the following quadratic number pattern: $64; 42; 24; ...$
3.1.5 Between which two consecutive terms of the quadratic number pattern will the difference be equal to 174?(2)
Show the memo (2 ticks)Memo
1. ✓
  Equate first difference to 174 $4 n - 26 = 174$
  $4 n = 200$
  $n = 50$
  1 mark · Use a pattern's first differences
2. ✓
  ConclusionBetween $T_{50}$ and $T_{51}$
  1 mark · Use a pattern's first differences
6. Question 3.3 · March 2015 · Provincial · 4 marks
Given the quadratic sequence: 4; 7; 14; 25; m
3.3 If the first difference between the two consecutive terms in the quadratic sequence is 87, determine the value of the two consecutive terms.(4)
Show the memo (5 ticks)Memo
1. ✓
  Formula for first differenceFirst difference is linear: $T_{n_{d i ff}} = 4 n - 1$
  0 marks · Use a pattern's first differences
2. ✓
  Set first difference equal to 87 $T_{n} - T_{n - 1} = 87$
  $4 n - 1 = 87$
  1 mark · Use a pattern's first differences
3. ✓
  n = 22 $4 n = 88 ⟹ n = 22$
  1 mark · Use a pattern's first differences
4. ✓
  T22 value $T_{22} = 2 (22)^{2} - 3 (22) + 5 = 907$
  1 mark · Use a quadratic general term
5. ✓
  T23 value $T_{23} = 2 (23)^{2} - 3 (23) + 5 = 994$
  1 mark · Use a quadratic general term

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