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 4 terms of the arithmetic series with first term a = 11 and common difference d = 5.
4 · 11 · 5 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 3.
4 · 9 · 3 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 2 and common difference d = 6.
8 · 2 · 6 · Arithmetic series sum
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 8 and common difference d = 7.
4 · 8 · 7 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
12 · 6 · 7 · Arithmetic series sum
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 15 and common difference d = 7.
8 · 15 · 7 · Arithmetic series sum
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 1 and common difference d = 8.
14 · 1 · 8 · Arithmetic series sum
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 7.
4 · 15 · 7 · Arithmetic series sum
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 11 and common difference d = 5.
10 · 11 · 5 · Arithmetic series sum
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 6.
8 · 8 · 6 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 10 and common difference d = 3.
10 · 10 · 3 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 9 and common difference d = 4.
10 · 9 · 4 · Arithmetic series sum

12 questions · Seed 52 · 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 4 terms of the arithmetic series with first term a = 11 and common difference d = 5.
74
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 11 + 3 × 5) = 74.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 3.
54
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 3) = 54.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 2 and common difference d = 6.
184
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 2 + 7 × 6) = 184.
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 8 and common difference d = 7.
74
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 8 + 3 × 7) = 74.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
534
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 6 + 11 × 7) = 534.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 15 and common difference d = 7.
316
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 15 + 7 × 7) = 316.
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 1 and common difference d = 8.
742
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 1 + 13 × 8) = 742.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 7.
102
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 15 + 3 × 7) = 102.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 11 and common difference d = 5.
335
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 11 + 9 × 5) = 335.
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 6.
232
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 8 + 7 × 6) = 232.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 10 and common difference d = 3.
235
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 10 + 9 × 3) = 235.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 9 and common difference d = 4.
270
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 9 + 9 × 4) = 270.

12 questions · Seed 52 · 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 4 terms of the arithmetic series with first term a = 11 and common difference d = 5.
4 · 11 · 5 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 3.
4 · 9 · 3 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 2 and common difference d = 6.
8 · 2 · 6 · Arithmetic series sum
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 8 and common difference d = 7.
4 · 8 · 7 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
12 · 6 · 7 · Arithmetic series sum
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 15 and common difference d = 7.
8 · 15 · 7 · Arithmetic series sum
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 1 and common difference d = 8.
14 · 1 · 8 · Arithmetic series sum
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 7.
4 · 15 · 7 · Arithmetic series sum
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 11 and common difference d = 5.
10 · 11 · 5 · Arithmetic series sum
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 6.
8 · 8 · 6 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 10 and common difference d = 3.
10 · 10 · 3 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 9 and common difference d = 4.
10 · 9 · 4 · Arithmetic series sum

12 questions · Seed 52 · 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 4 terms of the arithmetic series with first term a = 11 and common difference d = 5.
74
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 11 + 3 × 5) = 74.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 3.
54
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 3) = 54.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 2 and common difference d = 6.
184
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 2 + 7 × 6) = 184.
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 8 and common difference d = 7.
74
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 8 + 3 × 7) = 74.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
534
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 6 + 11 × 7) = 534.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 15 and common difference d = 7.
316
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 15 + 7 × 7) = 316.
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 1 and common difference d = 8.
742
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 1 + 13 × 8) = 742.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 7.
102
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 15 + 3 × 7) = 102.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 11 and common difference d = 5.
335
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 11 + 9 × 5) = 335.
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 6.
232
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 8 + 7 × 6) = 232.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 10 and common difference d = 3.
235
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 10 + 9 × 3) = 235.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 9 and common difference d = 4.
270
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 9 + 9 × 4) = 270.

12 questions · Seed 52 · Age guidance, not curriculum certification