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

12 questions · Seed 104731 · 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 12 terms of the arithmetic series with first term a = 4 and common difference d = 5.
378
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 4 + 11 × 5) = 378.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 9.
750
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 9) = 750.
3. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 5.
255
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 3 + 9 × 5) = 255.
4. Find the sum of the first 14 terms of the arithmetic series with first term a = 6 and common difference d = 4.
448
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 6 + 13 × 4) = 448.
5. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 4.
224
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 14 + 7 × 4) = 224.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 6 and common difference d = 9.
300
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 6 + 7 × 9) = 300.
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 4.
392
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 2 + 13 × 4) = 392.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 9.
70
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 4 + 3 × 9) = 70.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 8 and common difference d = 9.
485
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 8 + 9 × 9) = 485.
10. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 7.
355
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 4 + 9 × 7) = 355.
11. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 6.
552
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 6) = 552.
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 7 and common difference d = 8.
280
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 7 + 7 × 8) = 280.

12 questions · Seed 104731 · 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 12 terms of the arithmetic series with first term a = 4 and common difference d = 5.
12 · 4 · 5 · Arithmetic series sum
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 9.
12 · 13 · 9 · Arithmetic series sum
3. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 5.
10 · 3 · 5 · Arithmetic series sum
4. Find the sum of the first 14 terms of the arithmetic series with first term a = 6 and common difference d = 4.
14 · 6 · 4 · Arithmetic series sum
5. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 4.
8 · 14 · 4 · Arithmetic series sum
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 6 and common difference d = 9.
8 · 6 · 9 · Arithmetic series sum
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 4.
14 · 2 · 4 · Arithmetic series sum
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 9.
4 · 4 · 9 · Arithmetic series sum
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 8 and common difference d = 9.
10 · 8 · 9 · Arithmetic series sum
10. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 7.
10 · 4 · 7 · Arithmetic series sum
11. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 6.
12 · 13 · 6 · Arithmetic series sum
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 7 and common difference d = 8.
8 · 7 · 8 · Arithmetic series sum

12 questions · Seed 104731 · 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 12 terms of the arithmetic series with first term a = 4 and common difference d = 5.
378
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 4 + 11 × 5) = 378.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 9.
750
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 9) = 750.
3. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 5.
255
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 3 + 9 × 5) = 255.
4. Find the sum of the first 14 terms of the arithmetic series with first term a = 6 and common difference d = 4.
448
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 6 + 13 × 4) = 448.
5. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 4.
224
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 14 + 7 × 4) = 224.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 6 and common difference d = 9.
300
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 6 + 7 × 9) = 300.
7. Find the sum of the first 14 terms of the arithmetic series with first term a = 2 and common difference d = 4.
392
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 2 + 13 × 4) = 392.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 9.
70
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 4 + 3 × 9) = 70.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 8 and common difference d = 9.
485
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 8 + 9 × 9) = 485.
10. Find the sum of the first 10 terms of the arithmetic series with first term a = 4 and common difference d = 7.
355
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 4 + 9 × 7) = 355.
11. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 6.
552
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 6) = 552.
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 7 and common difference d = 8.
280
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 7 + 7 × 8) = 280.

12 questions · Seed 104731 · Age guidance, not curriculum certification