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

12 questions · Seed 53 · 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 = 7 and common difference d = 5.
414
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 7 + 11 × 5) = 414.
2. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 2.
168
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 14 + 7 × 2) = 168.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 4.
420
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 4) = 420.
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
684
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 8) = 684.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 7.
486
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 7) = 486.
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 8 and common difference d = 6.
658
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 8 + 13 × 6) = 658.
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 10 and common difference d = 9.
332
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 10 + 7 × 9) = 332.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 8.
174
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 9 + 5 × 8) = 174.
9. 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.
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 5.
525
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 5 + 13 × 5) = 525.
11. Find the sum of the first 4 terms of the arithmetic series with first term a = 13 and common difference d = 3.
70
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 13 + 3 × 3) = 70.
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 2.
96
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 2) = 96.

12 questions · Seed 53 · 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 = 7 and common difference d = 5.
12 · 7 · 5 · Arithmetic series sum
2. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 2.
8 · 14 · 2 · Arithmetic series sum
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 4.
12 · 13 · 4 · Arithmetic series sum
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
12 · 13 · 8 · Arithmetic series sum
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 7.
12 · 2 · 7 · Arithmetic series sum
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 8 and common difference d = 6.
14 · 8 · 6 · Arithmetic series sum
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 10 and common difference d = 9.
8 · 10 · 9 · Arithmetic series sum
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 8.
6 · 9 · 8 · Arithmetic series sum
9. 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
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 5.
14 · 5 · 5 · Arithmetic series sum
11. Find the sum of the first 4 terms of the arithmetic series with first term a = 13 and common difference d = 3.
4 · 13 · 3 · Arithmetic series sum
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 2.
8 · 5 · 2 · Arithmetic series sum

12 questions · Seed 53 · 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 = 7 and common difference d = 5.
414
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 7 + 11 × 5) = 414.
2. Find the sum of the first 8 terms of the arithmetic series with first term a = 14 and common difference d = 2.
168
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 14 + 7 × 2) = 168.
3. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 4.
420
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 4) = 420.
4. Find the sum of the first 12 terms of the arithmetic series with first term a = 13 and common difference d = 8.
684
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 13 + 11 × 8) = 684.
5. Find the sum of the first 12 terms of the arithmetic series with first term a = 2 and common difference d = 7.
486
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (12 ÷ 2)(2 × 2 + 11 × 7) = 486.
6. Find the sum of the first 14 terms of the arithmetic series with first term a = 8 and common difference d = 6.
658
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 8 + 13 × 6) = 658.
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 10 and common difference d = 9.
332
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 10 + 7 × 9) = 332.
8. Find the sum of the first 6 terms of the arithmetic series with first term a = 9 and common difference d = 8.
174
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (6 ÷ 2)(2 × 9 + 5 × 8) = 174.
9. 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.
10. Find the sum of the first 14 terms of the arithmetic series with first term a = 5 and common difference d = 5.
525
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 5 + 13 × 5) = 525.
11. Find the sum of the first 4 terms of the arithmetic series with first term a = 13 and common difference d = 3.
70
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 13 + 3 × 3) = 70.
12. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 2.
96
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 2) = 96.

12 questions · Seed 53 · Age guidance, not curriculum certification