Grade 11 Maths · Number Patterns, Sequences and Series · Find the smallest or largest term

Find the smallest or largest term Grade 11

Use the turning point of the quadratic general term to find the smallest or largest term of a pattern, remembering n must be a natural number (for example T_n = n^2 - 7n + 3 is smallest at n = 3 or 4, not 3,5).

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Grade 11 | Maximum & Minimum | Consecutive Term | Number PatternMagebaMaths

Quadratic number patterns grade 11: introduction and examplesKevinmathscience

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Question 3.3 · November 2025 · Paper 1 · National (DBE) · 3 marks

The depth of a torpedo below sea level forms a quadratic pattern, where

0

metres is at sea level. A submarine tracked a torpedo in one-second intervals.

The depth (in metres) that the torpedo reached is given in the table below. $Diagram for this question$

3.3 Calculate the maximum depth that the torpedo reached.(3)

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

More questions: find the smallest or largest term

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3. Question 2.2.3 · May/June 2022 · Paper 1 · National (DBE) · 4 marks
2.2 $75; 53; 35; 21; ...$ is a quadratic number pattern.
2.2.3 Determine the maximum value of the following number pattern:
$- 15; - \frac{53}{5}; - 7; - \frac{21}{5}; ...$ (4)
Show the memo (4 ticks)Memo
1. ✓
  METHOD 1: $n = 7$ Minimum value of $T_{n}$ :
  $n = - \frac{b}{2 a} = - \frac{( - 28 )}{2 ( 2 )}$
  $n = 7$
  1 mark · Find the smallest or largest term
2. ✓
  METHOD 1: Minimum value $= 3$ Minimum value of $T_{n} = 2 (7)^{2} - 28 (7) + 101 = 3$
  1 mark · Find the smallest or largest term
3. ✓
  METHOD 1: $- \frac{1}{5}$ of the old termEach term in the new pattern is $- \frac{1}{5}$ the value of the terms in the old pattern.
  1 mark · Use a quadratic general term
4. ✓
  METHOD 1: Maximum valueMaximum value of new pattern $= - \frac{3}{5}$
  1 mark · Use a quadratic general term
4. Practice · NavyBlue · 2 marks
Consider the quadratic pattern $- 3; 4; 9; 12; 13; \dots$
Show that $13$ is the largest term of the pattern.(2)
Show the memo (2 ticks)Memo
1. ✓
  Axis $n = - \frac{10}{2 ( - 1 )} = 5$
  1 mark · Find the smallest or largest term
2. ✓
  Largest term $T_{5} = - 25 + 50 - 12 = 13$
  1 mark · Find the smallest or largest term
5. Practice · NavyBlue · 2 marks
Consider the quadratic pattern $31; 22; 15; 10; \dots$
Determine the value of the smallest term.(2)
Show the memo (2 ticks)Memo
1. ✓
  Axis $n = - \frac{- 12}{2 ( 1 )} = 6$
  1 mark · Find the smallest or largest term
2. ✓
  Smallest term $T_{6} = 36 - 72 + 42 = 6$
  1 mark · Find the smallest or largest term
6. Practice · NavyBlue · 3 marks
Given $T_{n} = 3 n^{2} - 20 n + 40$ .
Determine the smallest term of the pattern.(3)
Show the memo (3 ticks)Memo
1. ✓
  Axis $n = \frac{20}{6} = 3 \frac{1}{3}$
  1 mark · Find the smallest or largest term
2. ✓
  Test neighbours $T_{3} = 27 - 60 + 40 = 7$
  $T_{4} = 48 - 80 + 40 = 8$
  1 mark · Find the smallest or largest term
3. ✓
  Smallest termThe smallest term is $T_{3} = 7$
  1 mark · Find the smallest or largest term

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