Grade 12 Maths · Number Patterns, Sequences and Series · Find terms from a sum formula

Find terms from a sum formula Grade 12

Find a term when you are given a formula for S_n by using T_n = S_n - S_n-1 (and T_1 = S_1), for example S_n = n^2 + 2n gives T_5 = 35 - 24 = 11.

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10) Use Sn to find Term | IntroKevinmathscience

Grade 12 Sequences and Series | Finding Tn When Sn is Given | Examples & PracticeYebo Tutor

How to calculate Tn from Sn grade 12ALAN THE MATHS TUTOR

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Question 3.2 · March 2022 · Provincial · 5 marks

3.2 The sum of the first

n

terms of a sequence is given by

S_{n} = 4 - 4 (\frac{1}{2})^{n}

. Calculate the first three terms.(5)

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More questions: find terms from a sum formula

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3. Question 2.2.2 · September 2026 · Paper 1 · Provincial · 4 marks
2.2 Given that: $\sum_{p = 1}^{n} (2 p + 2) = 990$
2.2.2 If $n = 30$ , show that $T_{n} = S_{n} - S_{n - 1}$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  Substitution $T_{n} = a + (n - 1) d$
  $T_{30} = 4 + 29 (2)$
  1 mark · Find a linear general term
2. ✓
  Answer $T_{30} = 62$
  1 mark · Find a linear general term
3. ✓
  Substitution $S_{n} - S_{n - 1} = S_{30} - S_{29} = 990 - [\frac{29}{2} [8 + 28 (2)]]$
  1 mark · Find terms from a sum formula
4. ✓
  Answer $= 990 - 928 = 62$
  $∴ T_{30} = S_{30} - S_{29}$
  1 mark · Find terms from a sum formula
4. Question 1.1.2 · March 2025 · Provincial · 2 marks
1.1 Given: The sum to $n$ terms of an arithmetic sequence is $S_{n} = 3 n^{2} - 5 n$ .
1.1.2 Determine the $2 2^{nd}$ term of this sequence.(2)
Show the memo (2 ticks)Memo
1. ✓
  Calculate sum to 22 terms $S_{22} = 3 (22)^{2} - 5 (22) = 1342$
  1 mark · Substitute into a formula
2. ✓
  Calculate term using difference of sums $T_{22} = S_{22} - S_{21}$
  $T_{22} = 1342 - 1218 = 124$
  1 mark · Find terms from a sum formula
5. Question 1.2 · March 2021 · Provincial · 3 marks
1.2 The sum of the first $p$ terms of a sequence of numbers is given by: $S_{p} = p (p + 1) (p + 2)$ . Calculate the value of $T_{20}$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Calculate S20 $S_{20} = 20 (20 + 1) (20 + 2) = 9240$
  1 mark · Substitute into a formula
2. ✓
  Calculate S19 $S_{19} = 19 (19 + 1) (19 + 2) = 7980$
  1 mark · Substitute into a formula
3. ✓
  Calculate T20 $T_{20} = S_{20} - S_{19}$
  $T_{20} = 9240 - 7980$
  $T_{20} = 1260$
  1 mark · Find terms from a sum formula
6. Practice · NavyBlue · 2 marks
The sum of the first $n$ terms of a series is given by $S_{n} = 2 n^{2} + 3 n$ .
Determine a formula for $T_{n}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Method $T_{n} = S_{n} - S_{n - 1} = 2 n^{2} + 3 n - [2 (n - 1)^{2} + 3 (n - 1)]$
  1 mark · Find terms from a sum formula
2. ✓
  Answer $= 2 n^{2} + 3 n - 2 n^{2} + 4 n - 2 - 3 n + 3$
  $T_{n} = 4 n + 1$
  1 mark · Find terms from a sum formula

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