Why do sequences matter in S5?

S5 uses sequences for patterns, savings and compound interest, and population growth, and the DSE paper one regularly tests the nth term and the sum of the first n terms; telling arithmetic from geometric is the key step.

Why write the nth term formula first?

Once the nth term is written, any term, any number of terms and any total can be found by substitution; adding terms one by one is slow and fails when there are many.

S5 Maths: Arithmetic and Geometric Sequences (Foundation, 10 Questions)

2026-11-08

Tutor Prep Guide · S5 Mathematics

Ten foundation items on the two nth term formulas, a + (n – 1)d for arithmetic and a x r^(n – 1) for geometric sequences, plus the sum formulas. Each has an answer and a one-line note.

Quick answer Answers in order: 39, -1, 49, 245, 140, 162, 96, 1/8, 124, 98. Write the formula first, then substitute, and bracket negative differences.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 25 minutes
Difficulty mix	Foundation 10
Chapter	Chapter: S5 Maths: Arithmetic and Geometric Sequences
Level	S5

02 Questions (10 items)

FoundationAn arithmetic sequence has first term 3 and common difference 4. Find the 10th term.
FoundationAn arithmetic sequence has first term 20 and common difference -3. Find the 8th term.
FoundationThe arithmetic sequence is 5, 9, 13, … Find the 12th term.
FoundationThe arithmetic sequence is 2, 7, 12, … Find the sum of the first 10 terms.
FoundationAn arithmetic sequence has first term 7 and common difference 3. Find the sum of the first 8 terms.
FoundationA geometric sequence has first term 2 and common ratio 3. Find the 5th term.
FoundationThe geometric sequence is 3, 6, 12, … Find the 6th term.
FoundationA geometric sequence has first term 1 and common ratio 1/2. Find the 4th term.
FoundationA geometric sequence has first term 4 and common ratio 2. Find the sum of the first 5 terms.
FoundationA sequence has nth term a_n = 5n – 2. Find the 20th term.

03 Answers and one-line notes

#	Answer	One-line note
1	39	The nth term is a + (n – 1)d, so the 10th term is 3 + 9 x 4 = 39.
2	-1	The 8th term is 20 + 7 x (-3) = 20 – 21 = -1; a negative difference makes the sequence fall.
3	49	The common difference is 9 – 5 = 4, so the 12th term is 5 + 11 x 4 = 49.
4	245	The sum is n/2 x [2a + (n – 1)d] = 5 x (4 + 45) = 245.
5	140	The sum of eight terms is 8/2 x (14 + 21) = 4 x 35 = 140.
6	162	The nth term is a x r^(n – 1), so the 5th term is 2 x 3^4 = 162.
7	96	The common ratio is 6 / 3 = 2, so the 6th term is 3 x 2^5 = 96.
8	1/8	The 4th term is 1 x (1/2)^3 = 1/8; a ratio below 1 makes the sequence decrease.
9	124	The sum is a(r^n – 1)/(r – 1) = 4 x 31 = 124.
10	98	Put n = 20 into the formula: 5 x 20 – 2 = 98.

04 What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

Find a tutor free Tutor Registration →

Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.