Sequences and Series Worksheet — GCSE — Intermediate

Sequences and Series worksheet for Key Stage 4 / GCSE (Ages 14-16). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 4 / GCSE (Ages 14-16)•Sequences and Seriesintermediate

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Exploring Sequences and Series

Key Stage 4 / GCSE (Ages 14-16) - Intermediate Level

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Instructions: This worksheet will help you understand and practice sequences and series. You'll explore arithmetic and geometric sequences, find specific terms, and solve related problems. Follow the instructions for each activity carefully.

Identifying Arithmetic Sequences

Examine the sequences provided and determine if they are arithmetic. If they are, identify the common difference. Write your answers in the boxes provided.

1. 3, 7, 11, 15, 19

2. 2, 4, 8, 16, 32

3. 10, 15, 20, 25, 30

4. 5, 10, 15, 25, 30

Finding the nth Term of an Arithmetic Sequence

Use the given formula for the nth term of an arithmetic sequence, a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference. Calculate the 10th term for each sequence.

1. Sequence: 2, 5, 8, 11, ...

2. Sequence: 7, 10, 13, 16, ...

3. Sequence: 4, 9, 14, 19, ...

Identifying Geometric Sequences

Determine if the sequences provided are geometric. If they are, identify the common ratio. Write your answers in the boxes provided.

1. 2, 6, 18, 54, 162

2. 5, 10, 20, 40, 80

3. 3, 9, 27, 81, 243

4. 1, 3, 5, 7, 9

Finding the nth Term of a Geometric Sequence

Use the formula for the nth term of a geometric sequence, a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. Calculate the 5th term for each sequence.

1. Sequence: 3, 6, 12, 24, ...

2. Sequence: 5, 15, 45, 135, ...

3. Sequence: 2, 8, 32, 128, ...

Sum of an Arithmetic Series

Calculate the sum of the first n terms of the arithmetic series using the formula S_n = n/2 * (a_1 + a_n). Solve for the given series.

1. Series: 1 + 3 + 5 + ... + 19

2. Series: 4 + 8 + 12 + ... + 40

3. Series: 7 + 14 + 21 + ... + 70

Sum of a Geometric Series

Calculate the sum of the first n terms of the geometric series using the formula S_n = a_1 * (1 - r^n) / (1 - r), where r ≠ 1. Solve for the given series.

1. Series: 2 + 6 + 18 + ... (first 4 terms)

2. Series: 3 + 9 + 27 + ... (first 5 terms)

3. Series: 5 + 15 + 45 + ... (first 3 terms)

Problem Solving with Sequences

Solve the following problems related to sequences. Show all your work clearly.

1. Find the 15th term of the sequence: 4, 9, 14, 19, ...

2. Determine the sum of the first 10 terms of the series: 3 + 6 + 9 + ...

3. If the 5th term of a geometric sequence is 48 and the common ratio is 2, find the first term.

Extended Writing: Sequences in Real Life

Write a detailed essay discussing how sequences and series are used in real-life applications. Provide examples such as financial calculations, computer algorithms, or natural patterns. [10 marks]

Answer Key

Activity 1: Yes, common difference = 4 ; No ; Yes, common difference = 5 ; No

Activity 2: 29 ; 34 ; 49

Activity 3: Yes, common ratio = 3 ; Yes, common ratio = 2 ; Yes, common ratio = 3 ; No

Activity 4: 48 ; 405 ; 512

Activity 5: 100 ; 220 ; 385

Activity 6: 80 ; 363 ; 155

Activity 7: 69 ; 165 ; 3

Activity 8: [Essay-based, no fixed answer]