MathsAges 16-18

Arithmetic series sum

Sum the first n terms of an arithmetic progression using Sₙ = (n ÷ 2)(2a + (n − 1)d). Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Arithmetic series sum

Take your time. Show your thinking.

1. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 9.
14 · 11 · 9 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 2 and common difference d = 4.
4 · 2 · 4 · Arithmetic series sum
3. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 9.
14 · 5 · 9 · Arithmetic series sum
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 9.
8 · 5 · 9 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
12 · 13 · 8 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 7.
6 · 13 · 7 · Arithmetic series sum
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 8.
12 · 14 · 8 · Arithmetic series sum
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 5.
6 · 2 · 5 · Arithmetic series sum
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 6.
8 · 9 · 6 · Arithmetic series sum
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 2.
14 · 2 · 2 · Arithmetic series sum
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 4.
8 · 1 · 4 · Arithmetic series sum
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
4 · 9 · 4 · Arithmetic series sum

12 questions · Seed 46 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Arithmetic series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 9.
973
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 11 + 13 × 9) = 973.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 2 and common difference d = 4.
32
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 2 + 3 × 4) = 32.
3. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 9.
889
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 5 + 13 × 9) = 889.
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 9.
292
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 9) = 292.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
684
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 8) = 684.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 7.
183
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 13 + 5 × 7) = 183.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 8.
696
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 14 + 11 × 8) = 696.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 5.
87
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 2 + 5 × 5) = 87.
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 6.
240
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 9 + 7 × 6) = 240.
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 2.
210
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 2 + 13 × 2) = 210.
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 4.
120
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 1 + 7 × 4) = 120.
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 4) = 60.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Arithmetic series sum

Take your time. Show your thinking.

1. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 9.
14 · 11 · 9 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 2 and common difference d = 4.
4 · 2 · 4 · Arithmetic series sum
3. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 9.
14 · 5 · 9 · Arithmetic series sum
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 9.
8 · 5 · 9 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
12 · 13 · 8 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 7.
6 · 13 · 7 · Arithmetic series sum
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 8.
12 · 14 · 8 · Arithmetic series sum
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 5.
6 · 2 · 5 · Arithmetic series sum
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 6.
8 · 9 · 6 · Arithmetic series sum
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 2.
14 · 2 · 2 · Arithmetic series sum
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 4.
8 · 1 · 4 · Arithmetic series sum
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
4 · 9 · 4 · Arithmetic series sum

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Arithmetic series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 9.
973
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 11 + 13 × 9) = 973.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 2 and common difference d = 4.
32
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 2 + 3 × 4) = 32.
3. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 9.
889
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 5 + 13 × 9) = 889.
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 9.
292
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 9) = 292.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
684
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 8) = 684.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 7.
183
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 13 + 5 × 7) = 183.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 8.
696
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 14 + 11 × 8) = 696.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 5.
87
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 2 + 5 × 5) = 87.
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 6.
240
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 9 + 7 × 6) = 240.
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 2.
210
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 2 + 13 × 2) = 210.
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 4.
120
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 1 + 7 × 4) = 120.
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 4.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 4) = 60.

12 questions · Seed 46 · Age guidance, not curriculum certification