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 10 terms of the arithmetic series with first term a = 4 and common difference d = 3.
10 · 4 · 3 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 12 and common difference d = 2.
4 · 12 · 2 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 5.
8 · 13 · 5 · Arithmetic series sum
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 4.
8 · 4 · 4 · Arithmetic series sum
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 15 and common difference d = 4.
14 · 15 · 4 · 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 = 8.
8 · 5 · 8 · Arithmetic series sum
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 5.
8 · 12 · 5 · Arithmetic series sum
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 7.
8 · 1 · 7 · Arithmetic series sum
9. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 4.
14 · 10 · 4 · Arithmetic series sum
10. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 8.
4 · 4 · 8 · 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 = 6.
4 · 9 · 6 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
10 · 5 · 2 · Arithmetic series sum

12 questions · Seed 47 · 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 10 terms of the arithmetic series with first term a = 4 and common difference d = 3.
175
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 4 + 9 × 3) = 175.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 12 and common difference d = 2.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 12 + 3 × 2) = 60.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 5.
244
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 13 + 7 × 5) = 244.
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 4.
144
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 4 + 7 × 4) = 144.
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 15 and common difference d = 4.
574
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 15 + 13 × 4) = 574.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 8.
264
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 8) = 264.
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 5.
236
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 5) = 236.
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 7.
204
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 1 + 7 × 7) = 204.
9. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 4.
504
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 10 + 13 × 4) = 504.
10. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 8.
64
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 4 + 3 × 8) = 64.
11. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 6.
72
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 6) = 72.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
140
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 5 + 9 × 2) = 140.

12 questions · Seed 47 · 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 10 terms of the arithmetic series with first term a = 4 and common difference d = 3.
10 · 4 · 3 · Arithmetic series sum
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 12 and common difference d = 2.
4 · 12 · 2 · Arithmetic series sum
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 5.
8 · 13 · 5 · Arithmetic series sum
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 4.
8 · 4 · 4 · Arithmetic series sum
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 15 and common difference d = 4.
14 · 15 · 4 · 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 = 8.
8 · 5 · 8 · Arithmetic series sum
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 5.
8 · 12 · 5 · Arithmetic series sum
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 7.
8 · 1 · 7 · Arithmetic series sum
9. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 4.
14 · 10 · 4 · Arithmetic series sum
10. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 8.
4 · 4 · 8 · 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 = 6.
4 · 9 · 6 · Arithmetic series sum
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
10 · 5 · 2 · Arithmetic series sum

12 questions · Seed 47 · 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 10 terms of the arithmetic series with first term a = 4 and common difference d = 3.
175
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 4 + 9 × 3) = 175.
2. Find the sum of the first 4 terms of the arithmetic series with first term a = 12 and common difference d = 2.
60
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 12 + 3 × 2) = 60.
3. Find the sum of the first 8 terms of the arithmetic series with first term a = 13 and common difference d = 5.
244
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 13 + 7 × 5) = 244.
4. Find the sum of the first 8 terms of the arithmetic series with first term a = 4 and common difference d = 4.
144
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 4 + 7 × 4) = 144.
5. Find the sum of the first 14 terms of the arithmetic series with first term a = 15 and common difference d = 4.
574
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 15 + 13 × 4) = 574.
6. Find the sum of the first 8 terms of the arithmetic series with first term a = 5 and common difference d = 8.
264
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 5 + 7 × 8) = 264.
7. Find the sum of the first 8 terms of the arithmetic series with first term a = 12 and common difference d = 5.
236
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 12 + 7 × 5) = 236.
8. Find the sum of the first 8 terms of the arithmetic series with first term a = 1 and common difference d = 7.
204
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (8 ÷ 2)(2 × 1 + 7 × 7) = 204.
9. Find the sum of the first 14 terms of the arithmetic series with first term a = 10 and common difference d = 4.
504
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (14 ÷ 2)(2 × 10 + 13 × 4) = 504.
10. Find the sum of the first 4 terms of the arithmetic series with first term a = 4 and common difference d = 8.
64
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 4 + 3 × 8) = 64.
11. Find the sum of the first 4 terms of the arithmetic series with first term a = 9 and common difference d = 6.
72
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (4 ÷ 2)(2 × 9 + 3 × 6) = 72.
12. Find the sum of the first 10 terms of the arithmetic series with first term a = 5 and common difference d = 2.
140
Sₙ = (n ÷ 2)(2a + (n − 1)d) = (10 ÷ 2)(2 × 5 + 9 × 2) = 140.

12 questions · Seed 47 · Age guidance, not curriculum certification