Grade 11 Maths · Number Patterns, Sequences and Series

Use a quadratic general term

Use a quadratic pattern formula to find a term or its position, for example if Tn = n² + 1, then T10 = 101.

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Quadratic Pattern Grade 11: ExamKevinmathscience

Quadratic Patterns -Grade 11 DBE Exam| Q4 | Number Patterns | Mlungisi NkosiMlungisi Nkosi Maths & Science

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Question 3.3 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

Given the quadratic sequence:

14; 9; 6; 5; ...

3.3 The value of

m

is added to each term in the quadratic sequence. Determine the values of

m

for which only the terms between

T_{1}

and

T_{7}

of the quadratic sequence will have negative values.(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 quadratic general term

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3. 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
4. Question 1.3 · March 2022 · Provincial · 2 marks
Given the quadratic sequence: $5; x; y; 29; \dots$ and its second constant difference is equal to $4$ .
1.3 Calculate the $5 0^{t h}$ term of the sequence.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute n=50 $T_{50} = 2 (50)^{2} - 2 (50) + 5$
  1 mark · Use a quadratic general term
2. ✓
  Calculate final value $T_{50} = 4905$
  1 mark · Use a quadratic general term
5. Question 1.3 · March 2021 · Provincial · 2 marks
Given the quadratic sequence: $44; 52; 64; 80; \dots$
1.3 Calculate the $3 0^{t h}$ term of the sequence.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute $n = 30$ $T_{30} = 2 (30)^{2} + 2 (30) + 40$
  1 mark · Use a quadratic general term
2. ✓
  Answer $T_{30} = 1900$
  1 mark · Use a quadratic general term
6. Question 3.1.3 · March 2018 · Provincial · 2 marks
3.1 Consider the following quadratic number pattern: $64; 42; 24; ...$
3.1.3 Calculate the value of the $2 0^{t h}$ term of this number pattern.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute n=20 $T_{20} = 2 (20)^{2} - 28 (20) + 90$
  1 mark · Use a quadratic general term
2. ✓
  Calculate value $= 330$
  1 mark · Use a quadratic general term

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