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 = 12 and common difference d = 4.
8 · 12 · 4 · Arithmetic series sum
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 6.
14 · 11 · 6 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 5.
12 · 1 · 5 · Arithmetic series sum
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 9.
12 · 12 · 9 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 9.
12 · 5 · 9 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 6.
6 · 2 · 6 · Arithmetic series sum
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 9.
10 · 13 · 9 · Arithmetic series sum
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 2.
8 · 9 · 2 · Arithmetic series sum
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 3.
6 · 5 · 3 · Arithmetic series sum
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 8.
6 · 13 · 8 · Arithmetic series sum
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 2.
8 · 8 · 2 · Arithmetic series sum
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 7.
12 · 1 · 7 · Arithmetic series sum

12 questions · Seed 104729 · 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 = 12 and common difference d = 4.
208
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 4) = 208.
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 6.
700
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 11 + 13 × 6) = 700.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 5.
342
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 1 + 11 × 5) = 342.
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 9.
738
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 12 + 11 × 9) = 738.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 9.
654
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 5 + 11 × 9) = 654.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 6.
102
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 2 + 5 × 6) = 102.
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 9.
535
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 9) = 535.
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 2.
128
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 9 + 7 × 2) = 128.
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 3.
75
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 3) = 75.
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 8.
198
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 13 + 5 × 8) = 198.
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 2.
120
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 8 + 7 × 2) = 120.
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 7.
474
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 1 + 11 × 7) = 474.

12 questions · Seed 104729 · 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 = 12 and common difference d = 4.
8 · 12 · 4 · Arithmetic series sum
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 6.
14 · 11 · 6 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 5.
12 · 1 · 5 · Arithmetic series sum
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 9.
12 · 12 · 9 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 9.
12 · 5 · 9 · Arithmetic series sum
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 6.
6 · 2 · 6 · Arithmetic series sum
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 9.
10 · 13 · 9 · Arithmetic series sum
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 2.
8 · 9 · 2 · Arithmetic series sum
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 3.
6 · 5 · 3 · Arithmetic series sum
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 8.
6 · 13 · 8 · Arithmetic series sum
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 2.
8 · 8 · 2 · Arithmetic series sum
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 7.
12 · 1 · 7 · Arithmetic series sum

12 questions · Seed 104729 · 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 = 12 and common difference d = 4.
208
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 4) = 208.
2. Find the sum of the first 14 terms of the arithmetic series with first term a = 11 and common difference d = 6.
700
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 11 + 13 × 6) = 700.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 5.
342
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 1 + 11 × 5) = 342.
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 12 and common difference d = 9.
738
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 12 + 11 × 9) = 738.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 5 and common difference d = 9.
654
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 5 + 11 × 9) = 654.
6. Find the sum of the first 6 terms of the arithmetic series with first term a = 2 and common difference d = 6.
102
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 2 + 5 × 6) = 102.
7. Find the sum of the first 10 terms of the arithmetic series with first term a = 13 and common difference d = 9.
535
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 13 + 9 × 9) = 535.
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 9 and common difference d = 2.
128
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 9 + 7 × 2) = 128.
9. Find the sum of the first 6 terms of the arithmetic series with first term a = 5 and common difference d = 3.
75
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 5 + 5 × 3) = 75.
10. Find the sum of the first 6 terms of the arithmetic series with first term a = 13 and common difference d = 8.
198
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 13 + 5 × 8) = 198.
11. Find the sum of the first 8 terms of the arithmetic series with first term a = 8 and common difference d = 2.
120
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 8 + 7 × 2) = 120.
12. Find the sum of the first 12 terms of the arithmetic series with first term a = 1 and common difference d = 7.
474
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 1 + 11 × 7) = 474.

12 questions · Seed 104729 · Age guidance, not curriculum certification