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 = 8 and common difference d = 6.
12 · 8 · 6 · Arithmetic series sum
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 4 and common difference d = 8.
14 · 4 · 8 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 6.
12 · 5 · 6 · Arithmetic series sum
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 14 and common difference d = 5.
4 · 14 · 5 · Arithmetic series sum
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 5.
4 · 1 · 5 · Arithmetic series sum
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 2.
12 · 4 · 2 · Arithmetic series sum
7. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 7.
4 · 4 · 7 · Arithmetic series sum
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 4.
6 · 14 · 4 · Arithmetic series sum
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 2.
6 · 6 · 2 · Arithmetic series sum
10. 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
11. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 7.
14 · 12 · 7 · 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 56 · 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 = 8 and common difference d = 6.
492
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 8 + 11 × 6) = 492.
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 4 and common difference d = 8.
784
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 4 + 13 × 8) = 784.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 6.
456
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 5 + 11 × 6) = 456.
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 14 and common difference d = 5.
86
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 14 + 3 × 5) = 86.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 5.
34
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 1 + 3 × 5) = 34.
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 2.
180
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 4 + 11 × 2) = 180.
7. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 7.
58
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 4 + 3 × 7) = 58.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 4.
144
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 14 + 5 × 4) = 144.
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 2.
66
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 6 + 5 × 2) = 66.
10. 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.
11. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 7.
805
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 12 + 13 × 7) = 805.
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 56 · 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 = 8 and common difference d = 6.
12 · 8 · 6 · Arithmetic series sum
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 4 and common difference d = 8.
14 · 4 · 8 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 6.
12 · 5 · 6 · Arithmetic series sum
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 14 and common difference d = 5.
4 · 14 · 5 · Arithmetic series sum
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 5.
4 · 1 · 5 · Arithmetic series sum
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 2.
12 · 4 · 2 · Arithmetic series sum
7. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 7.
4 · 4 · 7 · Arithmetic series sum
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 4.
6 · 14 · 4 · Arithmetic series sum
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 2.
6 · 6 · 2 · Arithmetic series sum
10. 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
11. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 7.
14 · 12 · 7 · 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 56 · 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 = 8 and common difference d = 6.
492
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 8 + 11 × 6) = 492.
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 4 and common difference d = 8.
784
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 4 + 13 × 8) = 784.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 6.
456
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 5 + 11 × 6) = 456.
4. Find the sum of the first 4 terms of the arithmetic series with first term a = 14 and common difference d = 5.
86
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 14 + 3 × 5) = 86.
5. Find the sum of the first 4 terms of the arithmetic series with first term a = 1 and common difference d = 5.
34
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 1 + 3 × 5) = 34.
6. Find the sum of the first 12 terms of the arithmetic series with first term a = 4 and common difference d = 2.
180
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 4 + 11 × 2) = 180.
7. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 7.
58
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 4 + 3 × 7) = 58.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 14 and common difference d = 4.
144
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 14 + 5 × 4) = 144.
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 6 and common difference d = 2.
66
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 6 + 5 × 2) = 66.
10. 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.
11. Find the sum of the first 14 terms of the arithmetic series with first term a = 12 and common difference d = 7.
805
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 12 + 13 × 7) = 805.
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 56 · Age guidance, not curriculum certification