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.

New variation Try interactive challenge Browse templates

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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

12 questions · Seed 50 · 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 = 3 and common difference d = 3.
315
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 3 + 13 × 3) = 315.
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 11 and common difference d = 6.
156
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 11 + 5 × 6) = 156.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 7 and common difference d = 4.
168
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 7 + 7 × 4) = 168.
4. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 3.
265
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 3) = 265.
5. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 4.
150
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 15 + 5 × 4) = 150.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 8.
204
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 14 + 5 × 8) = 204.
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 6.
126
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 6 + 5 × 6) = 126.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 11 and common difference d = 4.
68
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 11 + 3 × 4) = 68.
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 2.
160
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 13 + 7 × 2) = 160.
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 10 and common difference d = 3.
164
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 10 + 7 × 3) = 164.
11. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 9.
165
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 9) = 165.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 6 and common difference d = 7.
375
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 6 + 9 × 7) = 375.

12 questions · Seed 50 · 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 = 3 and common difference d = 3.
14 · 3 · 3 · Arithmetic series sum
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 11 and common difference d = 6.
6 · 11 · 6 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 7 and common difference d = 4.
8 · 7 · 4 · 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 = 3.
10 · 13 · 3 · Arithmetic series sum
5. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 4.
6 · 15 · 4 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 8.
6 · 14 · 8 · Arithmetic series sum
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 6.
6 · 6 · 6 · Arithmetic series sum
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 11 and common difference d = 4.
4 · 11 · 4 · Arithmetic series sum
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 2.
8 · 13 · 2 · Arithmetic series sum
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 10 and common difference d = 3.
8 · 10 · 3 · Arithmetic series sum
11. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 9.
6 · 5 · 9 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 6 and common difference d = 7.
10 · 6 · 7 · Arithmetic series sum

12 questions · Seed 50 · 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 = 3 and common difference d = 3.
315
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 3 + 13 × 3) = 315.
2. Find the sum of the first 6 terms of the arithmetic series with first term a = 11 and common difference d = 6.
156
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 11 + 5 × 6) = 156.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 7 and common difference d = 4.
168
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 7 + 7 × 4) = 168.
4. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 3.
265
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 3) = 265.
5. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 4.
150
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 15 + 5 × 4) = 150.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 8.
204
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 14 + 5 × 8) = 204.
7. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 6.
126
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 6 + 5 × 6) = 126.
8. Find the sum of the first 4 terms of the arithmetic series with first term a = 11 and common difference d = 4.
68
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 11 + 3 × 4) = 68.
9. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 2.
160
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 13 + 7 × 2) = 160.
10. Find the sum of the first 8 terms of the arithmetic series with first term a = 10 and common difference d = 3.
164
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 10 + 7 × 3) = 164.
11. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 9.
165
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 9) = 165.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 6 and common difference d = 7.
375
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 6 + 9 × 7) = 375.

12 questions · Seed 50 · Age guidance, not curriculum certification