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

12 questions · Seed 58 · 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 8 terms of the arithmetic series with first term a = 5 and common difference d = 6.
208
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 6) = 208.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 2.
156
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 2) = 156.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 7.
292
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 7) = 292.
4. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 9.
1015
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 14 + 13 × 9) = 1015.
5. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 3.
135
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 15 + 5 × 3) = 135.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 7.
236
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 7) = 236.
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 6 and common difference d = 2.
150
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 6 + 9 × 2) = 150.
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
534
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 6 + 11 × 7) = 534.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 14 and common difference d = 8.
500
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 14 + 9 × 8) = 500.
10. 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.
11. 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.
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 7.
594
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 11 + 11 × 7) = 594.

12 questions · Seed 58 · 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 8 terms of the arithmetic series with first term a = 5 and common difference d = 6.
8 · 5 · 6 · Arithmetic series sum
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 2.
12 · 2 · 2 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 7.
8 · 12 · 7 · Arithmetic series sum
4. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 9.
14 · 14 · 9 · 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 = 3.
6 · 15 · 3 · Arithmetic series sum
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 7.
8 · 5 · 7 · Arithmetic series sum
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 6 and common difference d = 2.
10 · 6 · 2 · Arithmetic series sum
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
12 · 6 · 7 · Arithmetic series sum
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 14 and common difference d = 8.
10 · 14 · 8 · Arithmetic series sum
10. 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
11. 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
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 7.
12 · 11 · 7 · Arithmetic series sum

12 questions · Seed 58 · 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 8 terms of the arithmetic series with first term a = 5 and common difference d = 6.
208
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 6) = 208.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 2.
156
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 2) = 156.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 7.
292
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 7) = 292.
4. Find the sum of the first 14 terms of the arithmetic series with first term a = 14 and common difference d = 9.
1015
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 14 + 13 × 9) = 1015.
5. Find the sum of the first 6 terms of the arithmetic series with first term a = 15 and common difference d = 3.
135
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 15 + 5 × 3) = 135.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 7.
236
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 7) = 236.
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 6 and common difference d = 2.
150
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 6 + 9 × 2) = 150.
8. Find the sum of the first 12 terms of the arithmetic series with first term a = 6 and common difference d = 7.
534
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 6 + 11 × 7) = 534.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 14 and common difference d = 8.
500
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 14 + 9 × 8) = 500.
10. 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.
11. 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.
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 7.
594
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 11 + 11 × 7) = 594.

12 questions · Seed 58 · Age guidance, not curriculum certification