Why does the nth term formula use n minus 1?

The first term already needs no difference, so the nth term has n minus 1 differences.

How do you reverse the common difference from two terms?

Subtract the terms and divide by the gap in position numbers, for example five differences between the 8th and 3rd terms.

When does an infinite geometric sum exist?

Only when the ratio has absolute value below 1; the sum is the first term divided by 1 minus the ratio.

Why use the square of the middle number for three geometric terms?

The outer terms multiply to the square of the middle one, which with the sum fixes both numbers.

S5 Maths sequences paper 4: error drills

2026-11-10

Tutor Prep Guide · S5 Maths Arithmetic and Geometric Sequences

Ten items target common slips: counting one term too many, reversing from two terms, infinite geometric sums, closed-form sums and three-term geometric setups.

Direct answers　Items 01 to 03 use the nth term and the geometric term formula, 04 to 06 cover partial sums, solving for n and reversing from two terms, 07 to 09 an infinite sum, a closed-form sum and three-term geometric setups, and 10 the off-by-one in counting terms.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S5 Maths Arithmetic and Geometric Sequences
Level	S5

02　Questions (10 items)

FoundationAn arithmetic sequence has first term 7 and common difference 4. Find the 15th term.
FoundationFor the sequence 3, 8, 13, find the 20th term.
FoundationA geometric sequence has first term 5 and common ratio 2. Find the 6th term.
IntermediateFind the sum of the first 12 terms of 4 + 7 + 10 + and so on.
IntermediateThe first n terms of 3 + 6 + 12 + and so on sum to 189. Find n.
IntermediateAn arithmetic sequence has third term 11 and eighth term 31. Find the common difference and the 15th term.
ChallengeFind the sum of the infinite geometric series 8 + 4 + 2 + and so on.
ChallengeThe sum of the first n terms of an arithmetic sequence is n squared plus 3n. Find the 10th term.
ChallengeThree numbers form a geometric sequence. The middle number is 6 and the sum is 26. Find the other two.
Error redoAn arithmetic sequence has first term 6 and common difference 5. A student writes the 10th term as 6 + 10 times 5 = 56. What is the correct value?

03　Answers and one-line notes

#	Answer	One-line note
1	63	The 15th term is the first term plus 14 differences, that is 7 + 14 times 4.
2	98	The common difference is 5, so the 20th term is 3 + 19 times 5.
3	160	The 6th term is 5 times 2 to the power 5.
4	246	Pair the ends or use the formula 12 over 2 times the quantity 8 + 33.
5	n = 6	From 3 times the quantity 2 to the n minus 1 equal to 189, 2 to the n is 64.
6	Difference 4, 15th term 59	Five differences amount to 20, giving the difference, then the first term is 3.
7	16	The ratio is one half, so the sum is 8 divided by 1 minus one half.
8	22	The first term is 4 and the difference is 2, so the 10th term is 4 + 9 times 2.
9	2 and 18	Let the outer numbers be x and y; xy = 36 together with x + y = 20 gives the answer.
10	51	From the first term to the 10th only nine differences are added, that is 6 + 9 times 5.

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.

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