Sequences (arithmetic sequences) — KCSE Mathematics

KCSE Mathematics · 115 practice questions · 4 syllabus objectives

35 easy42 medium38 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Identify an arithmetic sequence; find the first term and common difference from a sequence or given terms

Apply the formula for the nth term of an AP: Tₙ = a + (n–1)d, and find the sum using Sₙ = n/2(2a + (n–1)d)

Solve problems involving arithmetic progressions in real-life contexts (savings, salary increments, stacking)

Sequences (arithmetic sequences)

Sample Questions

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1
easySHORT ANSWER2 marks

A certain savings plan starts with an initial deposit of KES 500 and increases by KES 100 each month. Identify the amount saved in the 6th month. (2 marks)

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Part (a) — 2 marks
T₆ = 500 + (6 - 1) × 100 (1 mk)
Amount saved in the 6th month is KES 1000 (1 mk)
2
easySHORT ANSWER4 marks

Calculate the sum of the first 15 terms of an arithmetic series where the first term is 2 and the common difference is 4. (4 marks)

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Part (a) — 4 marks
Use the formula Sₙ = n/2(2a + (n - 1)d) (1 mk)
Substitute n = 15, a = 2, d = 4 into the formula (1 mk)
Calculate S₁₅ = 15/2(2*2 + (15 - 1)*4) (1 mk)
Find S₁₅ = 15/2(4 + 56) = 15/2(60) = 450 (1 mk)
3
easySHORT ANSWER3 marks

Explain how to find the 10th term of an arithmetic sequence where the first term is 5 and the common difference is 3. (3 marks)

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Part (a) — 3 marks
Use the formula Tₙ = a + (n - 1)d (1 mk)
Substitute a = 5, n = 10, and d = 3 into the formula (1 mk)
Calculate T₁₀ = 5 + (10 - 1) * 3 = 32 (1 mk)
4

State the formula to find the sum of the first n terms of an arithmetic progression. (2 marks)

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Why Practise Sequences (arithmetic sequences)?

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