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

12 questions · Seed 44 · 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 = 13 and common difference d = 9.
1001
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 13 + 13 × 9) = 1001.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 6.
564
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 14 + 11 × 6) = 564.
3. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 3.
22
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 1 + 3 × 3) = 22.
4. 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.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 10 and common difference d = 3.
58
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 10 + 3 × 3) = 58.
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 2.
204
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 6 + 11 × 2) = 204.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 8 and common difference d = 3.
294
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 8 + 11 × 3) = 294.
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 2.
152
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 2) = 152.
9. Find the sum of the first 4 terms of the arithmetic series with first term a = 13 and common difference d = 9.
106
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 13 + 3 × 9) = 106.
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 10 and common difference d = 2.
252
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 10 + 11 × 2) = 252.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 2.
120
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 3 + 9 × 2) = 120.
12. 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.

12 questions · Seed 44 · 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 = 13 and common difference d = 9.
14 · 13 · 9 · Arithmetic series sum
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 6.
12 · 14 · 6 · Arithmetic series sum
3. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 3.
4 · 1 · 3 · Arithmetic series sum
4. 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
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 10 and common difference d = 3.
4 · 10 · 3 · Arithmetic series sum
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 2.
12 · 6 · 2 · Arithmetic series sum
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 8 and common difference d = 3.
12 · 8 · 3 · Arithmetic series sum
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 2.
8 · 12 · 2 · Arithmetic series sum
9. Find the sum of the first 4 terms of the arithmetic series with first term a = 13 and common difference d = 9.
4 · 13 · 9 · Arithmetic series sum
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 10 and common difference d = 2.
12 · 10 · 2 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 2.
10 · 3 · 2 · Arithmetic series sum
12. 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

12 questions · Seed 44 · 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 = 13 and common difference d = 9.
1001
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 13 + 13 × 9) = 1001.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 6.
564
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 14 + 11 × 6) = 564.
3. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 3.
22
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 1 + 3 × 3) = 22.
4. 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.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 10 and common difference d = 3.
58
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 10 + 3 × 3) = 58.
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 2.
204
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 6 + 11 × 2) = 204.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 8 and common difference d = 3.
294
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 8 + 11 × 3) = 294.
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 2.
152
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 2) = 152.
9. Find the sum of the first 4 terms of the arithmetic series with first term a = 13 and common difference d = 9.
106
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 13 + 3 × 9) = 106.
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 10 and common difference d = 2.
252
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 10 + 11 × 2) = 252.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 2.
120
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 3 + 9 × 2) = 120.
12. 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.

12 questions · Seed 44 · Age guidance, not curriculum certification