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

12 questions · Seed 54 · 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 12 terms of the arithmetic series with first term a = 2 and common difference d = 9.
618
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 9) = 618.
2. Find the sum of the first 10 terms of the arithmetic series with first term a = 15 and common difference d = 3.
285
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 15 + 9 × 3) = 285.
3. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 3.
78
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 15 + 3 × 3) = 78.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 2.
36
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 1 + 5 × 2) = 36.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 5.
42
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 3 + 3 × 5) = 42.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 6.
144
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 9 + 5 × 6) = 144.
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 11 and common difference d = 9.
340
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 11 + 7 × 9) = 340.
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 9.
642
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 4 + 11 × 9) = 642.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 11 and common difference d = 6.
380
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 11 + 9 × 6) = 380.
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 4.
432
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 14 + 11 × 4) = 432.
11. 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.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 9.
435
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 3 + 9 × 9) = 435.

12 questions · Seed 54 · 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 = 2 and common difference d = 9.
12 · 2 · 9 · Arithmetic series sum
2. Find the sum of the first 10 terms of the arithmetic series with first term a = 15 and common difference d = 3.
10 · 15 · 3 · Arithmetic series sum
3. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 3.
4 · 15 · 3 · Arithmetic series sum
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 2.
6 · 1 · 2 · Arithmetic series sum
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 5.
4 · 3 · 5 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 6.
6 · 9 · 6 · Arithmetic series sum
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 11 and common difference d = 9.
8 · 11 · 9 · Arithmetic series sum
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 9.
12 · 4 · 9 · 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 = 6.
10 · 11 · 6 · Arithmetic series sum
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 4.
12 · 14 · 4 · Arithmetic series sum
11. 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
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 9.
10 · 3 · 9 · Arithmetic series sum

12 questions · Seed 54 · 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 = 2 and common difference d = 9.
618
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 9) = 618.
2. Find the sum of the first 10 terms of the arithmetic series with first term a = 15 and common difference d = 3.
285
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 15 + 9 × 3) = 285.
3. Find the sum of the first 4 terms of the arithmetic series with first term a = 15 and common difference d = 3.
78
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 15 + 3 × 3) = 78.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 1 and common difference d = 2.
36
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 1 + 5 × 2) = 36.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 3 and common difference d = 5.
42
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 3 + 3 × 5) = 42.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 6.
144
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 9 + 5 × 6) = 144.
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 11 and common difference d = 9.
340
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 11 + 7 × 9) = 340.
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 9.
642
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 4 + 11 × 9) = 642.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 11 and common difference d = 6.
380
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 11 + 9 × 6) = 380.
10. Find the sum of the first 12 terms of the arithmetic series with first term a = 14 and common difference d = 4.
432
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 14 + 11 × 4) = 432.
11. 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.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 3 and common difference d = 9.
435
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 3 + 9 × 9) = 435.

12 questions · Seed 54 · Age guidance, not curriculum certification