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

12 questions · Seed 45 · 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 = 13 and common difference d = 5.
82
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 13 + 3 × 5) = 82.
2. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 3.
156
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 9 + 7 × 3) = 156.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 3 and common difference d = 3.
234
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 3 + 11 × 3) = 234.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 7.
141
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 6 + 5 × 7) = 141.
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 6.
400
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 6) = 400.
6. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 9.
90
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 9) = 90.
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 5.
81
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 1 + 5 × 5) = 81.
8. 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.
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 9.
364
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 14 + 7 × 9) = 364.
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 3 and common difference d = 8.
564
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 3 + 11 × 8) = 564.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 8 and common difference d = 3.
215
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 8 + 9 × 3) = 215.
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 5.
180
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 5) = 180.

12 questions · Seed 45 · 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 = 13 and common difference d = 5.
4 · 13 · 5 · Arithmetic series sum
2. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 3.
8 · 9 · 3 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 3 and common difference d = 3.
12 · 3 · 3 · Arithmetic series sum
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 7.
6 · 6 · 7 · Arithmetic series sum
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 6.
10 · 13 · 6 · Arithmetic series sum
6. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 9.
4 · 9 · 9 · Arithmetic series sum
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 5.
6 · 1 · 5 · Arithmetic series sum
8. 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
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 9.
8 · 14 · 9 · Arithmetic series sum
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 3 and common difference d = 8.
12 · 3 · 8 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 8 and common difference d = 3.
10 · 8 · 3 · Arithmetic series sum
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 5.
8 · 5 · 5 · Arithmetic series sum

12 questions · Seed 45 · 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 = 13 and common difference d = 5.
82
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 13 + 3 × 5) = 82.
2. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 3.
156
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 9 + 7 × 3) = 156.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 3 and common difference d = 3.
234
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 3 + 11 × 3) = 234.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 7.
141
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 6 + 5 × 7) = 141.
5. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 6.
400
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 6) = 400.
6. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 9.
90
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 9) = 90.
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 5.
81
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 1 + 5 × 5) = 81.
8. 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.
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 9.
364
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 14 + 7 × 9) = 364.
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 3 and common difference d = 8.
564
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 3 + 11 × 8) = 564.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 8 and common difference d = 3.
215
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 8 + 9 × 3) = 215.
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 5.
180
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 5) = 180.

12 questions · Seed 45 · Age guidance, not curriculum certification