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

12 questions · Seed 104734 · 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 4 terms of the arithmetic series with first term a = 8 and common difference d = 5.
62
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 8 + 3 × 5) = 62.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 2.
288
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 2) = 288.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 7.
228
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 4 + 7 × 7) = 228.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 12 and common difference d = 8.
192
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 12 + 5 × 8) = 192.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 11 and common difference d = 3.
62
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 11 + 3 × 3) = 62.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 4 and common difference d = 5.
99
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 4 + 5 × 5) = 99.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 8.
660
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 11 + 11 × 8) = 660.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 7 and common difference d = 4.
102
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 7 + 5 × 4) = 102.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 2 and common difference d = 7.
335
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 2 + 9 × 7) = 335.
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 9.
189
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 9 + 5 × 9) = 189.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 14 and common difference d = 3.
275
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 14 + 9 × 3) = 275.
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 5 and common difference d = 5.
50
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 5 + 3 × 5) = 50.

12 questions · Seed 104734 · 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 4 terms of the arithmetic series with first term a = 8 and common difference d = 5.
4 · 8 · 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 = 2.
12 · 13 · 2 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 7.
8 · 4 · 7 · Arithmetic series sum
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 12 and common difference d = 8.
6 · 12 · 8 · Arithmetic series sum
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 11 and common difference d = 3.
4 · 11 · 3 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 4 and common difference d = 5.
6 · 4 · 5 · Arithmetic series sum
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 8.
12 · 11 · 8 · Arithmetic series sum
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 7 and common difference d = 4.
6 · 7 · 4 · Arithmetic series sum
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 2 and common difference d = 7.
10 · 2 · 7 · Arithmetic series sum
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 9.
6 · 9 · 9 · Arithmetic series sum
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 14 and common difference d = 3.
10 · 14 · 3 · Arithmetic series sum
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 5 and common difference d = 5.
4 · 5 · 5 · Arithmetic series sum

12 questions · Seed 104734 · 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 4 terms of the arithmetic series with first term a = 8 and common difference d = 5.
62
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 8 + 3 × 5) = 62.
2. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 2.
288
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 2) = 288.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 7.
228
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 4 + 7 × 7) = 228.
4. Find the sum of the first 6 terms of the arithmetic series with first term a = 12 and common difference d = 8.
192
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 12 + 5 × 8) = 192.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 11 and common difference d = 3.
62
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 11 + 3 × 3) = 62.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 4 and common difference d = 5.
99
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 4 + 5 × 5) = 99.
7. Find the sum of the first 12 terms of the arithmetic series with first term a = 11 and common difference d = 8.
660
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 11 + 11 × 8) = 660.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 7 and common difference d = 4.
102
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 7 + 5 × 4) = 102.
9. Find the sum of the first 10 terms of the arithmetic series with first term a = 2 and common difference d = 7.
335
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 2 + 9 × 7) = 335.
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 9.
189
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 9 + 5 × 9) = 189.
11. Find the sum of the first 10 terms of the arithmetic series with first term a = 14 and common difference d = 3.
275
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 14 + 9 × 3) = 275.
12. Find the sum of the first 4 terms of the arithmetic series with first term a = 5 and common difference d = 5.
50
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 5 + 3 × 5) = 50.

12 questions · Seed 104734 · Age guidance, not curriculum certification