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 6 terms of the arithmetic series with first term a = 8 and common difference d = 9.
6 · 8 · 9 · Arithmetic series sum
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 8 and common difference d = 4.
6 · 8 · 4 · 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 12 terms of the arithmetic series with first term a = 9 and common difference d = 5.
12 · 9 · 5 · Arithmetic series sum
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 5.
10 · 4 · 5 · Arithmetic series sum
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 3 and common difference d = 4.
14 · 3 · 4 · Arithmetic series sum
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 9.
12 · 11 · 9 · Arithmetic series sum
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 8.
4 · 3 · 8 · Arithmetic series sum
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 9.
6 · 15 · 9 · Arithmetic series sum
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 8.
6 · 5 · 8 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 2.
10 · 13 · 2 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
10 · 5 · 2 · Arithmetic series sum

12 questions · Seed 104730 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 16-18

Arithmetic series sum

Answers and reasoning. Review before teaching.

1. Find the sum of the first 6 terms of the arithmetic series with first term a = 8 and common difference d = 9.
183
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 8 + 5 × 9) = 183.
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 8 and common difference d = 4.
108
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 8 + 5 × 4) = 108.
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 12 terms of the arithmetic series with first term a = 9 and common difference d = 5.
438
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 9 + 11 × 5) = 438.
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 5.
265
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 4 + 9 × 5) = 265.
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 3 and common difference d = 4.
406
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 3 + 13 × 4) = 406.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 9.
726
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 11 + 11 × 9) = 726.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 8.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 3 + 3 × 8) = 60.
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 9.
225
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 15 + 5 × 9) = 225.
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 8.
150
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 8) = 150.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 2.
220
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 2) = 220.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
140
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 5 + 9 × 2) = 140.

12 questions · Seed 104730 · 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 6 terms of the arithmetic series with first term a = 8 and common difference d = 9.
6 · 8 · 9 · Arithmetic series sum
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 8 and common difference d = 4.
6 · 8 · 4 · 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 12 terms of the arithmetic series with first term a = 9 and common difference d = 5.
12 · 9 · 5 · Arithmetic series sum
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 5.
10 · 4 · 5 · Arithmetic series sum
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 3 and common difference d = 4.
14 · 3 · 4 · Arithmetic series sum
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 9.
12 · 11 · 9 · Arithmetic series sum
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 8.
4 · 3 · 8 · Arithmetic series sum
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 9.
6 · 15 · 9 · Arithmetic series sum
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 8.
6 · 5 · 8 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 2.
10 · 13 · 2 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
10 · 5 · 2 · Arithmetic series sum

12 questions · Seed 104730 · 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 6 terms of the arithmetic series with first term a = 8 and common difference d = 9.
183
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 8 + 5 × 9) = 183.
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 8 and common difference d = 4.
108
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 8 + 5 × 4) = 108.
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 12 terms of the arithmetic series with first term a = 9 and common difference d = 5.
438
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 9 + 11 × 5) = 438.
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 5.
265
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 4 + 9 × 5) = 265.
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 3 and common difference d = 4.
406
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 3 + 13 × 4) = 406.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 9.
726
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 11 + 11 × 9) = 726.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 8.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 3 + 3 × 8) = 60.
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 9.
225
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 15 + 5 × 9) = 225.
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 8.
150
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 8) = 150.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 2.
220
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 2) = 220.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
140
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 5 + 9 × 2) = 140.

12 questions · Seed 104730 · Age guidance, not curriculum certification